Pub Date : 2025-09-18DOI: 10.1016/j.camwa.2025.09.008
Dong Yan , Xin-Jie Huang , Guiyuan Ma , Xin-Jiang He
We study an American option pricing problem with liquidity risks and transaction fees. As endogenous transaction costs, liquidity risks of the underlying asset are modeled by a mean-reverting process. Transaction fees are exogenous transaction costs and are assumed to be proportional to the trading amount, with the long-run liquidity level depending on the proportional transaction costs rate. Two nonlinear partial differential equations are established to characterize the option values for the holder and the writer, respectively. To illustrate the impact of these transaction costs on option prices and optimal exercise prices, we apply the alternating direction implicit method to solve the linear complementarity problem numerically. Finally, we conduct model calibration from market data via maximum likelihood estimation, and find that our model incorporating liquidity risks outperforms the Leland model significantly.
{"title":"Pricing American options with exogenous and endogenous transaction costs","authors":"Dong Yan , Xin-Jie Huang , Guiyuan Ma , Xin-Jiang He","doi":"10.1016/j.camwa.2025.09.008","DOIUrl":"10.1016/j.camwa.2025.09.008","url":null,"abstract":"<div><div>We study an American option pricing problem with liquidity risks and transaction fees. As endogenous transaction costs, liquidity risks of the underlying asset are modeled by a mean-reverting process. Transaction fees are exogenous transaction costs and are assumed to be proportional to the trading amount, with the long-run liquidity level depending on the proportional transaction costs rate. Two nonlinear partial differential equations are established to characterize the option values for the holder and the writer, respectively. To illustrate the impact of these transaction costs on option prices and optimal exercise prices, we apply the alternating direction implicit method to solve the linear complementarity problem numerically. Finally, we conduct model calibration from market data via maximum likelihood estimation, and find that our model incorporating liquidity risks outperforms the Leland model significantly.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 85-101"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.camwa.2025.09.004
A. Chakraborty , J. Muñoz-Matute , L. Demkowicz , J. Grosek
In this article, we propose a modified nonlinear Schrödinger equation for modeling pulse propagation in optical waveguides. The proposed model bifurcates into a system of elliptic and hyperbolic equations depending on waveguide parameters. The proposed model leads to a stable first-order system of equations, distinguishing itself from the canonical nonlinear Schrödinger equation. We have employed the space-time discontinuous Petrov-Galerkin finite element method to discretize the first-order system of equations. We present a stability analysis for both the elliptic and hyperbolic systems of equations and demonstrate the stability of the proposed model through several numerical examples on space-time meshes.
{"title":"A space-time discontinuous Petrov-Galerkin finite element formulation for a modified Schrödinger equation for laser pulse propagation in waveguides","authors":"A. Chakraborty , J. Muñoz-Matute , L. Demkowicz , J. Grosek","doi":"10.1016/j.camwa.2025.09.004","DOIUrl":"10.1016/j.camwa.2025.09.004","url":null,"abstract":"<div><div>In this article, we propose a modified nonlinear Schrödinger equation for modeling pulse propagation in optical waveguides. The proposed model bifurcates into a system of elliptic and hyperbolic equations depending on waveguide parameters. The proposed model leads to a stable first-order system of equations, distinguishing itself from the canonical nonlinear Schrödinger equation. We have employed the space-time discontinuous Petrov-Galerkin finite element method to discretize the first-order system of equations. We present a stability analysis for both the elliptic and hyperbolic systems of equations and demonstrate the stability of the proposed model through several numerical examples on space-time meshes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 67-84"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.camwa.2025.09.002
Zhixin Liu , Minghui Song , Yuhang Zhang
In this paper, we propose and analyze an efficient, linearized, fully discrete scheme for the nonlinear, strongly damped Klein-Gordon equation on polygonal meshes. The numerical scheme uses a conforming virtual element method for spatial discretization and a modified leapfrog (central finite difference) scheme for time discretization, with the nonlinear term is treated semi-implicitly. We first prove that the proposed scheme is energy dissipative in the sense of discrete energy, and then the stability of the numerical solution in the -norm is established using mathematical induction, which plays an important role in handling the nonlinear term. By applying the boundedness of the numerical solution and the Sobolev embedding inequality, we derive the optimal error estimate of order without imposing any ratio restrictions between the time step τ and the mesh size h. Additionally, we remark that the leapfrog virtual element scheme can be applied to some more complex nonlinear damped wave equations. Finally, some numerical examples are provided to confirm the theoretical results.
{"title":"Convergence analysis of an energy-stable linearized virtual element method for the strongly damped Klein-Gordon equation","authors":"Zhixin Liu , Minghui Song , Yuhang Zhang","doi":"10.1016/j.camwa.2025.09.002","DOIUrl":"10.1016/j.camwa.2025.09.002","url":null,"abstract":"<div><div>In this paper, we propose and analyze an efficient, linearized, fully discrete scheme for the nonlinear, strongly damped Klein-Gordon equation on polygonal meshes. The numerical scheme uses a conforming virtual element method for spatial discretization and a modified leapfrog (central finite difference) scheme for time discretization, with the nonlinear term <span><math><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi></math></span> is treated semi-implicitly. We first prove that the proposed scheme is energy dissipative in the sense of discrete energy, and then the stability of the numerical solution in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm is established using mathematical induction, which plays an important role in handling the nonlinear term. By applying the boundedness of the numerical solution and the Sobolev embedding inequality, we derive the optimal <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> error estimate of order <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>+</mo><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> without imposing any ratio restrictions between the time step <em>τ</em> and the mesh size <em>h</em>. Additionally, we remark that the leapfrog virtual element scheme can be applied to some more complex nonlinear damped wave equations. Finally, some numerical examples are provided to confirm the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 49-66"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.camwa.2025.09.016
W. Huang, X.B. Yan, J.X. Liao, L.K. Feng, P.H. Wen
This paper presents a fundamental solution for a double-curvature simply supported shell, incorporating three concentrated forces and two bending moments. It introduces the reference domain concept and formulates fictitious load boundary integral equations using both constant and linear elements. These equations are developed in the Laplace transform domain for both static and dynamic problems. The key contribution of this study is the development of the Regular Boundary Element Method (RBEM) based on the new fundamental solution. The reference domain includes the real structure’s configuration, and a system of linear equations is established with fictitious forces and moments as unknowns. These equations are derived from traction and displacement boundary conditions. To obtain all physical values in the time domain, the Durbin’s Laplace inverse technique is applied. The accuracy and reliability of the proposed method are evaluated through four numerical examples, with results compared against exact solutions or the finite element method.
{"title":"Regular boundary element method for composite shear deformable plate and shell","authors":"W. Huang, X.B. Yan, J.X. Liao, L.K. Feng, P.H. Wen","doi":"10.1016/j.camwa.2025.09.016","DOIUrl":"10.1016/j.camwa.2025.09.016","url":null,"abstract":"<div><div>This paper presents a fundamental solution for a double-curvature simply supported shell, incorporating three concentrated forces and two bending moments. It introduces the reference domain concept and formulates fictitious load boundary integral equations using both constant and linear elements. These equations are developed in the Laplace transform domain for both static and dynamic problems. The key contribution of this study is the development of the Regular Boundary Element Method (RBEM) based on the new fundamental solution. The reference domain includes the real structure’s configuration, and a system of linear equations is established with fictitious forces and moments as unknowns. These equations are derived from traction and displacement boundary conditions. To obtain all physical values in the time domain, the Durbin’s Laplace inverse technique is applied. The accuracy and reliability of the proposed method are evaluated through four numerical examples, with results compared against exact solutions or the finite element method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 106-126"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.camwa.2025.09.003
Akira Furukawa
In this paper, we apply orthogonal matching pursuit (OMP) to the source point selection in the method of fundamental solutions (MFS) and discuss its effectiveness. The proposed method initially places an excess number of source points relative to the collocation points within the complementary domain of the analysis region and then selects the source points that efficiently reduce the residual of the system of equations. We apply the proposed method to two-dimensional elastic wave scattering by a rectangular cavity, a well-known challenging problem in MFS analysis. Numerical examples demonstrate the effectiveness of the proposed method by comparing its performance with the conventional MFS using truncated singular value decomposition (TSVD). The proposed method provides solutions that more accurately satisfy the traction-free boundary conditions compared to the conventional method, indicating its potential advantages.
{"title":"Source point selection in the MFS using orthogonal matching pursuit: Two-dimensional elastic wave scattering by a rectangular cavity","authors":"Akira Furukawa","doi":"10.1016/j.camwa.2025.09.003","DOIUrl":"10.1016/j.camwa.2025.09.003","url":null,"abstract":"<div><div>In this paper, we apply orthogonal matching pursuit (OMP) to the source point selection in the method of fundamental solutions (MFS) and discuss its effectiveness. The proposed method initially places an excess number of source points relative to the collocation points within the complementary domain of the analysis region and then selects the source points that efficiently reduce the residual of the system of equations. We apply the proposed method to two-dimensional elastic wave scattering by a rectangular cavity, a well-known challenging problem in MFS analysis. Numerical examples demonstrate the effectiveness of the proposed method by comparing its performance with the conventional MFS using truncated singular value decomposition (TSVD). The proposed method provides solutions that more accurately satisfy the traction-free boundary conditions compared to the conventional method, indicating its potential advantages.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 80-105"},"PeriodicalIF":2.5,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-17DOI: 10.1016/j.camwa.2025.09.005
Mi-Young Kim
This study aims to derive and analyze an a posteriori error estimator for the solution of the discontinuous Galerkin method with Lagrange multiplier (DGLM) for the elliptic problems with nonhomogeneous Dirichlet boundary condition for g in . A general version of the DGLM method is derived. Strong stability of the solution of the DGLM method is proved. Edgewise iterative scheme for the general DGLM method is described.
{"title":"A posteriori error estimate of the discontinuous Galerkin method with Lagrange multiplier for elliptic problems","authors":"Mi-Young Kim","doi":"10.1016/j.camwa.2025.09.005","DOIUrl":"10.1016/j.camwa.2025.09.005","url":null,"abstract":"<div><div>This study aims to derive and analyze an a posteriori error estimator for the solution of the discontinuous Galerkin method with Lagrange multiplier (DGLM) for the elliptic problems with nonhomogeneous Dirichlet boundary condition <span><math><mi>u</mi><mo>=</mo><mi>g</mi></math></span> for <em>g</em> in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>(</mo><mo>∂</mo><mi>Ω</mi><mo>)</mo></math></span>. A general version of the DGLM method is derived. Strong stability of the solution of the DGLM method is proved. Edgewise iterative scheme for the general DGLM method is described.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 38-48"},"PeriodicalIF":2.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-17DOI: 10.1016/j.camwa.2025.09.006
Wenlong He , Jiwei Zhang
Many multiphysics processes of fluid-solid interaction within a porous medium can be described by the Biot-Brinkman model to account for the effects of viscosity in fluid flow. By introducing the auxiliary variables, we can transform the original problem into two generalized Stokes equations. The generalized Stokes equations incorporate a built-in mechanism to circumvent the Poisson locking for the continuous Galerkin method. Subsequently, we establish an energy law and provide a priori estimates for the reformulated problem. Well-posedness is demonstrated using the standard Galerkin method in conjunction with a compactness argument. After that, we develop stable mixed finite element algorithms for the reformulated problem. Influenced by Lamé constant λ, we design three finite element pairs for the proposed algorithms and present the corresponding error estimates. Numerical tests are conducted to validate the theoretical results.
{"title":"Stability and convergence analysis of mixed finite element approximations for a Biot-Brinkman model","authors":"Wenlong He , Jiwei Zhang","doi":"10.1016/j.camwa.2025.09.006","DOIUrl":"10.1016/j.camwa.2025.09.006","url":null,"abstract":"<div><div>Many multiphysics processes of fluid-solid interaction within a porous medium can be described by the Biot-Brinkman model to account for the effects of viscosity in fluid flow. By introducing the auxiliary variables, we can transform the original problem into two generalized Stokes equations. The generalized Stokes equations incorporate a built-in mechanism to circumvent the Poisson locking for the continuous Galerkin method. Subsequently, we establish an energy law and provide a priori estimates for the reformulated problem. Well-posedness is demonstrated using the standard Galerkin method in conjunction with a compactness argument. After that, we develop stable mixed finite element algorithms for the reformulated problem. Influenced by Lamé constant <em>λ</em>, we design three finite element pairs for the proposed algorithms and present the corresponding error estimates. Numerical tests are conducted to validate the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 22-37"},"PeriodicalIF":2.5,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-16DOI: 10.1016/j.camwa.2025.08.032
Xiaoyu Duan , Zihan Wang , Hengbin An , Zeyao Mo
In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. The mortar finite element method is usually employed to discretize the variational form on the meshed contact surfaces, yielding a large-scale discretized saddle point system. Due to the indefiniteness of the discretized system, it is a challenge to solve the saddle point algebraic system. For two-dimensional tied contact problem, we develop an efficient algorithm based on degree-of-freedom (DOF) condensation. In this approach, a DOFs elimination process is first performed by exploiting the tridiagonal structure of the mortar matrix. The reduced linear system, now smaller in scale and symmetric positive definite (SPD), is then solved using the preconditioned conjugate gradient (PCG) method. Numerical results demonstrate the effectiveness of the algorithm.
{"title":"A DOFs condensation based algorithm for solving saddle point systems in 2D contact computation","authors":"Xiaoyu Duan , Zihan Wang , Hengbin An , Zeyao Mo","doi":"10.1016/j.camwa.2025.08.032","DOIUrl":"10.1016/j.camwa.2025.08.032","url":null,"abstract":"<div><div>In contact mechanics computation, the constraint conditions on the contact surfaces are typically enforced by the Lagrange multiplier method, resulting in a saddle point system. The mortar finite element method is usually employed to discretize the variational form on the meshed contact surfaces, yielding a large-scale discretized saddle point system. Due to the indefiniteness of the discretized system, it is a challenge to solve the saddle point algebraic system. For two-dimensional tied contact problem, we develop an efficient algorithm based on degree-of-freedom (DOF) condensation. In this approach, a DOFs elimination process is first performed by exploiting the tridiagonal structure of the mortar matrix. The reduced linear system, now smaller in scale and symmetric positive definite (SPD), is then solved using the preconditioned conjugate gradient (PCG) method. Numerical results demonstrate the effectiveness of the algorithm.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 64-79"},"PeriodicalIF":2.5,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Weather derivatives are financial tools that use a weather index as the underlying asset to provide protection against non-catastrophic weather events. In this article, we propose a physics-informed neural network (PINN) approach for pricing weather derivatives associated with two standard processes: the Ornstein-Uhlenbeck process and the Ornstein-Uhlenbeck process with jump-diffusions. PINNs are a scientific machine learning method specifically designed to address problems related to partial differential equations (PDEs).
To apply the PINN technique for jump-diffusion, we convert the partial integro-differential equation into a PDE using integral discretization. We randomly select training data points within the domain and utilize the transformed PDE along with the initial and boundary conditions to construct the loss function. For the neurons in the hidden layer, we employ the hyperbolic tangent function (tanh) as the activation function. The weights of the network connection are optimized using the L-BFGS algorithm.
We will conduct numerical experiments to evaluate the efficiency of the proposed technique. Additionally, we compare our method with conventional numerical approaches to show that our technique serves as an effective alternative to existing pricing methods for weather derivatives. Finally, we will examine a real-world case study where the model's parameters are determined using precipitation data.
{"title":"Physics-informed neural network for option pricing weather derivatives model","authors":"Saurabh Bansal , Pradanya Boro , Srinivasan Natesan","doi":"10.1016/j.camwa.2025.09.001","DOIUrl":"10.1016/j.camwa.2025.09.001","url":null,"abstract":"<div><div>Weather derivatives are financial tools that use a weather index as the underlying asset to provide protection against non-catastrophic weather events. In this article, we propose a physics-informed neural network (PINN) approach for pricing weather derivatives associated with two standard processes: the Ornstein-Uhlenbeck process and the Ornstein-Uhlenbeck process with jump-diffusions. PINNs are a scientific machine learning method specifically designed to address problems related to partial differential equations (PDEs).</div><div>To apply the PINN technique for jump-diffusion, we convert the partial integro-differential equation into a PDE using integral discretization. We randomly select training data points within the domain and utilize the transformed PDE along with the initial and boundary conditions to construct the loss function. For the neurons in the hidden layer, we employ the hyperbolic tangent function (tanh) as the activation function. The weights of the network connection are optimized using the L-BFGS algorithm.</div><div>We will conduct numerical experiments to evaluate the efficiency of the proposed technique. Additionally, we compare our method with conventional numerical approaches to show that our technique serves as an effective alternative to existing pricing methods for weather derivatives. Finally, we will examine a real-world case study where the model's parameters are determined using precipitation data.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"200 ","pages":"Pages 1-21"},"PeriodicalIF":2.5,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-12DOI: 10.1016/j.camwa.2025.07.035
Jan Martin Nordbotten , Eirik Keilegavlen
In this paper, we construct a simple and robust two-point finite volume discretization applicable to isotropic linearized elasticity, valid also in the incompressible Stokes’ limit. The discretization is based only on co-located, cell-centered variables, and has a minimal discretization stencil, using only the two neighboring cells to a face to calculate numerical stresses and fluxes. The discretization naturally couples to finite volume discretizations of flow, providing a stable discretization of poroelasticity.
We show well-posedness of a weak statement of the continuous formulation in appropriate Hilbert spaces, and identify the appropriate weighted norms for the problem. For the discrete approximations, we prove stability and convergence, both of which are robust in terms of the material parameters. Numerical experiments in 3D support the theoretical results, and provide additional insight into the practical performance of the discretization.
{"title":"Two-point stress approximation: A simple and robust finite volume method for linearized (poro-)elasticity and Stokes flow","authors":"Jan Martin Nordbotten , Eirik Keilegavlen","doi":"10.1016/j.camwa.2025.07.035","DOIUrl":"10.1016/j.camwa.2025.07.035","url":null,"abstract":"<div><div>In this paper, we construct a simple and robust two-point finite volume discretization applicable to isotropic linearized elasticity, valid also in the incompressible Stokes’ limit. The discretization is based only on co-located, cell-centered variables, and has a minimal discretization stencil, using only the two neighboring cells to a face to calculate numerical stresses and fluxes. The discretization naturally couples to finite volume discretizations of flow, providing a stable discretization of poroelasticity.</div><div>We show well-posedness of a weak statement of the continuous formulation in appropriate Hilbert spaces, and identify the appropriate weighted norms for the problem. For the discrete approximations, we prove stability and convergence, both of which are robust in terms of the material parameters. Numerical experiments in 3D support the theoretical results, and provide additional insight into the practical performance of the discretization.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"197 ","pages":"Pages 259-294"},"PeriodicalIF":2.5,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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