Computational Methods in Applied Mathematics最新文献

英文中文

Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability 非等温耦合相场系统的变分法：结构保持与非线性稳定性

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-09-02 DOI: 10.1515/cmam-2023-0274

Aaron Brunk, Oliver Habrich, Timileyin David Oyedeji, Yangyiwei Yang, Bai-Xiang Xu

A Cahn–Hilliard–Allen–Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem with respect to the inverse of temperature, we proposed and analysed a structure-preserving approximation for the semi-discretisation in space and then a fully discrete approximation using conforming finite elements and time-stepping methods. We prove structure-preserving property and discrete stability using relative entropy methods for the semi-discrete and fully discrete case. The theoretical results are illustrated by numerical experiments.

我们研究了与传热方程耦合的 Cahn-Hilliard-Allen-Cahn 相场模型，特别是全非对角流动矩阵。在根据温度倒数对问题进行重新表述后，我们提出并分析了空间半离散化的结构保持近似方法，然后使用符合有限元和时间步进方法提出了完全离散的近似方法。我们使用相对熵方法证明了半离散和全离散情况下的结构保持特性和离散稳定性。数值实验对理论结果进行了说明。

引用次数: 0

A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines 用于旋转电机涡流近似的时空有限元方法

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-09-02 DOI: 10.1515/cmam-2024-0033

Peter Gangl, Mario Gobrial, Olaf Steinbach

In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in a space-time domain. Based on the Babuška–Nečas theory we prove unique solvability both for the continuous variational formulation and for a standard Galerkin finite element discretization in the space-time domain. This approach allows for an adaptive resolution of the solution both in space and time, but it requires the solution of the overall system of algebraic equations. While the use of parallel solution algorithms seems to be mandatory, this also allows for a parallelization simultaneously in space and time. This approach is used for the eddy current approximation of the Maxwell equations which results in an elliptic-parabolic interface problem. Numerical results for linear and nonlinear constitutive material relations confirm the applicability and accuracy of the proposed approach.

在本文中，我们提出并分析了一种用于旋转电机数值模拟的时空有限元方法，其中有限元网格固定在时空域中。基于 Babuška-Nečas 理论，我们证明了连续变量公式和标准 Galerkin 有限元离散时空域的唯一可解性。这种方法可以在空间和时间上自适应地求解，但需要求解整个代数方程系统。虽然似乎必须使用并行求解算法，但这也允许在空间和时间上同时进行并行化。这种方法用于麦克斯韦方程的涡流近似，其结果是椭圆-抛物线界面问题。线性和非线性材料构成关系的数值结果证实了所提方法的适用性和准确性。

引用次数: 0

An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod 构建振动棒的逆矩阵特征值问题

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-08-02 DOI: 10.1515/cmam-2024-0001

Hanif Mirzaei, Vahid Abbasnavaz, Kazem Ghanbari

The free longitudinal vibrations of a rod are described by a differential equation of the form <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>P</m:mi> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mi>y</m:mi> <m:mo>′</m:mo> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>′</m:mo> </m:msup> <m:mo>+</m:mo> <m:mi>λ</m:mi> <m:mi>P</m:mi> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mi>y</m:mi> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {(P(x)yprime)^{prime}+lambda P(x)y(x)=0} , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>P</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>x</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> {P(x)} is the cross section area at point x and λ is an eigenvalue parameter. In this paper, first we discretize this differential equation by using the finite difference method to obtain a matrix eigenvalue problem of the form <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi>𝐀</m:mi> <m:mo>⁢</m:mo> <m:mi>Y</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mi mathvariant="normal">Λ</m:mi> <m:mo>⁢</m:mo> <m:mi>𝐁</m:mi> <m:mo>⁢</m:mo> <m:mi>Y</m:mi> </m:mrow> </m:mrow> </m:math> {mathbf{A}Y=Lambdamathbf{B}Y} , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>𝐀</m:mi> </m:math> {mathbf{A}} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>𝐁</m:mi> </m:math> {mathbf{B}} are Jacobi and diagonal matrices dependent to cross section <jats:alter

杆的自由纵向振动由一个微分方程描述，其形式为 ( P ( x ) y ′ ) ′ + λ P ( x ) y ( x ) = 0 {(P(x)yprime)^{prime}+lambda P(x)y(x)=0} 。其中，P ( x ) {P(x)} 是 x 点的横截面积，λ 是特征值参数。本文首先用有限差分法对该微分方程进行离散化，得到一个矩阵特征值问题，其形式为 𝐀 Y = Λ 𝐁 Y {mathbf{A}Y=Lambdamathbf{B}Y} 、其中，𝐀 {mathbf{A}} 和 𝐁 {mathbf{B}} 分别是与横截面 P ( x ) {P(x)} 相关的雅可比矩阵和对角矩阵。然后，我们通过修正所得矩阵特征值问题的特征值来估计杆方程的特征值。我们给出了一种基于修正思想的方法，通过求解逆矩阵特征值问题来构建横截面 P ( x ) {P(x)}。我们给出了一些数值示例来说明所提方法的效率。结果表明，该方法的收敛阶数为 O ( h 2 ) {O(h^{2})} 。

引用次数: 0

On Error Estimates of a discontinuous Galerkin Method of the Boussinesq System of Equations 论布西内斯克方程组非连续伽勒金方法的误差估算

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-07-10 DOI: 10.1515/cmam-2023-0202

Saumya Bajpai, Debendra Kumar Swain

In this paper, we propose and analyze a discontinuous Galerkin finite element method for solving the transient Boussinesq incompressible heat conducting fluid flow equations. This method utilizes an upwind approach to handle the nonlinear convective terms effectively. We discuss new a priori bounds for the semidiscrete discontinuous Galerkin approximations. Furthermore, we establish optimal a priori error estimates for the semidiscrete discontinuous Galerkin velocity approximation in L 2

mathbf{L}^{2}

and energy norms, the temperature approximation in L 2

L^{2}

and energy norms and pressure approximation in L 2

L^{2}

-norm for t > 0

t>0

. Additionally, under the smallness assumption on the data, we prove uniform in time error estimates. We also consider a backward Euler scheme for full discretization and derive fully discrete error estimates. Finally, we provide numerical examples to support the theoretical conclusions.

本文提出并分析了一种非连续 Galerkin 有限元方法，用于求解瞬态 Boussinesq 不可压缩导热流体流动方程。该方法利用上风法有效处理非线性对流项。我们讨论了半离散非连续 Galerkin 近似的新先验边界。此外，我们还为 L 2 mathbf{L}^{2} 和能量规范下的半离散不连续 Galerkin 速度近似、L 2 L^{2} 和能量规范下的温度近似以及 L 2 L^{2} -规范下的压力近似建立了最佳先验误差估计。 -t > 0 t>0 时的 L 2 L^{2} 和能量规范中的温度近似和 L 2 L^{2} 中的压力近似。此外，在数据较小的假设下，我们证明了时间误差估计的一致性。我们还考虑了完全离散化的后向欧拉方案，并推导出完全离散的误差估计值。最后，我们提供了数值示例来支持理论结论。

{"title":"On Error Estimates of a discontinuous Galerkin Method of the Boussinesq System of Equations","authors":"Saumya Bajpai, Debendra Kumar Swain","doi":"10.1515/cmam-2023-0202","DOIUrl":"https://doi.org/10.1515/cmam-2023-0202","url":null,"abstract":"In this paper, we propose and analyze a discontinuous Galerkin finite element method for solving the transient Boussinesq incompressible heat conducting fluid flow equations. This method utilizes an upwind approach to handle the nonlinear convective terms effectively. We discuss new a priori bounds for the semidiscrete discontinuous Galerkin approximations. Furthermore, we establish optimal a priori error estimates for the semidiscrete discontinuous Galerkin velocity approximation in <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi mathvariant=\"bold\">L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> mathbf{L}^{2} and energy norms, the temperature approximation in <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> L^{2} and energy norms and pressure approximation in <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>L</m:mi> <m:mn>2</m:mn> </m:msup> </m:math> L^{2} -norm for <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>t</m:mi> <m:mo>></m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> t>0 . Additionally, under the smallness assumption on the data, we prove uniform in time error estimates. We also consider a backward Euler scheme for full discretization and derive fully discrete error estimates. Finally, we provide numerical examples to support the theoretical conclusions.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2) 应用数学中的计算方法（CMAM 2022 会议，第 2 部分）

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-07-01 DOI: 10.1515/cmam-2024-0090

Michael Feischl, Dirk Praetorius, Michele Ruggeri

This paper introduces the contents of the second of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue.

本文介绍了与 2022 年 8 月 29 日至 9 月 2 日在维也纳举行的第九届应用数学计算方法国际会议相关的两期特刊中的第二期特刊的内容。它对特刊中所有 12 篇论文的主题和亮点进行了评论。

引用次数: 0

Space-Time FEM for the Vectorial Wave Equation under Consideration of Ohm’s Law 考虑欧姆定律的矢量波方程时空有限元模型

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-06-25 DOI: 10.1515/cmam-2023-0079

Julia I. M. Hauser

The ability to deal with complex geometries and to go to higher orders is the main advantage of space-time finite element methods. Therefore, we want to develop a solid background from which we can construct appropriate space-time methods. In this paper, we will treat time as another space direction, which is the main idea of space-time methods. First, we will briefly discuss how exactly the vectorial wave equation is derived from Maxwell’s equations in a space-time structure, taking into account Ohm’s law. Then we will derive a space-time variational formulation for the vectorial wave equation using different trial and test spaces. This paper has two main goals. First, we prove unique solvability for the resulting Galerkin–Petrov variational formulation. Second, we analyze the discrete equivalent of the equation in a tensor product and show conditional stability, i.e., under a CFL condition. Understanding the vectorial wave equation and the corresponding space-time finite element methods is crucial for improving the existing theory of Maxwell’s equations and paves the way to computations of more complicated electromagnetic problems.

时空有限元方法的主要优势在于能够处理复杂的几何图形并达到更高的阶次。因此，我们希望建立一个坚实的背景，在此基础上构建适当的时空方法。在本文中，我们将把时间视为另一个空间方向，这也是时空方法的主要思想。首先，我们将简要讨论在时空结构中，考虑到欧姆定律，究竟如何从麦克斯韦方程导出矢量波方程。然后，我们将利用不同的试验和测试空间推导出矢量波方程的时空变分公式。本文有两个主要目标。首先，我们将证明所得到的 Galerkin-Petrov 变式的唯一可解性。其次，我们分析了该方程在张量积中的离散等价物，并展示了条件稳定性，即在 CFL 条件下的稳定性。理解矢量波方程和相应的时空有限元方法对于改进现有的麦克斯韦方程理论至关重要，并为计算更复杂的电磁问题铺平了道路。

引用次数: 0

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem 用于 p 拉普拉斯问题的各向异性自适应有限元

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-06-25 DOI: 10.1515/cmam-2022-0205

Paride Passelli, Marco Picasso

The p-Laplacian problem - ∇ ⋅ ( ( μ + | ∇ ⁡ u | p - 2 ) ⁢ ∇ ⁡ u ) = f

{-nablacdot((mu+|nabla u|^{p-2})nabla u)=f}

is considered, where μ is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher order terms, to the error in a quasi-norm. The involved constants being independent of μ, the solution, the mesh size and aspect ratio. An adaptive algorithm is proposed and numerical results are presented when p = 3

{p=3}

. From this model problem, we propose a simplified error estimator and use it in the framework of an industrial application, namely a nonlinear Navier–Stokes problem arising from aluminium electrolysis.

考虑了 p-拉普拉斯问题-∇ ⋅ ( ( μ + | ∇ u | p - 2 ) ∇ u ) = f {-nablacdot((mu+|nabla u|^{p-2})nabla u)=f} ，其中 μ 是给定的正数。提出了一个基于各向异性后验残差的误差估计器。该误差估计器在高阶项上等同于准正则误差。所涉及的常数与 μ、解、网格尺寸和纵横比无关。我们提出了一种自适应算法，并给出了 p = 3 {p=3} 时的数值结果。根据这一模型问题，我们提出了一个简化的误差估计器，并将其用于工业应用框架，即铝电解产生的非线性纳维-斯托克斯问题。

{"title":"Anisotropic Adaptive Finite Elements for a p-Laplacian Problem","authors":"Paride Passelli, Marco Picasso","doi":"10.1515/cmam-2022-0205","DOIUrl":"https://doi.org/10.1515/cmam-2022-0205","url":null,"abstract":"The p-Laplacian problem <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mrow> <m:mo>-</m:mo> <m:mrow> <m:mo>∇</m:mo> <m:mo>⋅</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mrow> <m:mi>μ</m:mi> <m:mo>+</m:mo> <m:msup> <m:mrow> <m:mo stretchy=\"false\">|</m:mo> <m:mrow> <m:mo>∇</m:mo> <m:mo>⁡</m:mo> <m:mi>u</m:mi> </m:mrow> <m:mo stretchy=\"false\">|</m:mo> </m:mrow> <m:mrow> <m:mi>p</m:mi> <m:mo>-</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> <m:mo>⁢</m:mo> <m:mrow> <m:mo>∇</m:mo> <m:mo>⁡</m:mo> <m:mi>u</m:mi> </m:mrow> </m:mrow> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo>=</m:mo> <m:mi>f</m:mi> </m:mrow> </m:math> {-nablacdot((mu+|nabla u|^{p-2})nabla u)=f} is considered, where μ is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher order terms, to the error in a quasi-norm. The involved constants being independent of μ, the solution, the mesh size and aspect ratio. An adaptive algorithm is proposed and numerical results are presented when <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>p</m:mi> <m:mo>=</m:mo> <m:mn>3</m:mn> </m:mrow> </m:math> {p=3} . From this model problem, we propose a simplified error estimator and use it in the framework of an industrial application, namely a nonlinear Navier–Stokes problem arising from aluminium electrolysis.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"2016 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On an Optimal AFEM for Elastoplasticity 论弹塑性的最优 AFEM

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-06-25 DOI: 10.1515/cmam-2024-0052

Miriam Schönauer, Andreas Schröder

In this paper, optimal convergence for an adaptive finite element algorithm for elastoplasticity is considered. To this end, the proposed adaptive algorithm is established within the abstract framework of the axioms of adaptivity [C. Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity, Comput. Math. Appl. 67 2014, 6, 1195–1253], which provides a specific proceeding to prove the optimal convergence of the scheme. The proceeding is based on verifying four axioms, which ensure the optimal convergence. The verification is done by using results from [C. Carstensen, A. Schröder and S. Wiedemann, An optimal adaptive finite element method for elastoplasticity, Numer. Math. 132 2016, 1, 131–154], which presents an alternative approach to optimality without explicitly relying on the axioms

本文考虑了弹塑性自适应有限元算法的最佳收敛性。为此，本文在自适应公理的抽象框架内建立了所提出的自适应算法[C. Carstensen, M. Feischl, M. Page and D. Praetorius, 《弹性力学》]。Carstensen, M. Feischl, M. Page and D. Praetorius, Axioms of adaptivity, Comput.Math.67 2014, 6, 1195-1253]，它提供了证明方案最优收敛性的具体程序。该程序基于对四个公理的验证，这四个公理确保了最优收敛性。验证是利用 [C. Carstensen, A. Sch.Carstensen, A. Schröder and S. Wiedemann, An optimal adaptive finite element method for elastoplasticity, Numer.Math.132 2016, 1, 131-154] 中的结果，它提出了另一种不明确依赖公理的最优方法

引用次数: 0

A Novel Fully Decoupled Scheme for the MHD System with Variable Density 针对密度可变的 MHD 系统的新型完全解耦方案

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-04-29 DOI: 10.1515/cmam-2024-0004

Zhaowei Wang, Danxia Wang, Hongen Jia

In this paper, we first establish a novel first-order, fully decoupled, unconditionally stable time discretization scheme for the MHD system with variable density. This scheme successfully decouples all the coupling terms by combining the gauge-Uzawa method and the scalar auxiliary variable (SAV) method. And we prove its unconditional energy stability. Then we give the first-order finite element scheme and its implementation. Furthermore, we perform a rigorous error analysis of the proposed numerical scheme. Finally, we perform some numerical experiments to demonstrate the effectiveness of the decoupling scheme.

在本文中，我们首先为密度可变的 MHD 系统建立了一个新颖的一阶、完全解耦和无条件稳定的时间离散化方案。该方案结合了 gauge-Uzawa 方法和标量辅助变量（SAV）方法，成功地解耦了所有耦合项。我们证明了它的无条件能量稳定性。然后，我们给出了一阶有限元方案及其实现。此外，我们还对所提出的数值方案进行了严格的误差分析。最后，我们进行了一些数值实验来证明解耦方案的有效性。

引用次数: 0

Quadratic Discontinuous Galerkin Finite Element Methods for the Unilateral Contact Problem 单边接触问题的二次非连续 Galerkin 有限元方法

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics

Pub Date : 2024-04-23 DOI: 10.1515/cmam-2023-0015

Kamana Porwal, Tanvi Wadhawan

In this article, we employ discontinuous Galerkin methods for the finite element approximation of the frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We first develop a posteriori error estimates in the energy norm wherein, the reliability and efficiency of the proposed a posteriori error estimator is addressed. The suitable construction of the discrete Lagrange multiplier 𝝀 𝒉

{boldsymbol{lambda_{h}}}

and some intermediate operators play a key role in developing a posteriori error analysis. Further, we establish an optimal a priori error estimates under the appropriate regularity assumption on the exact solution 𝒖

{boldsymbol{u}}

. Numerical results presented on uniform and adaptive meshes illustrate and confirm the theoretical findings.

在本文中，我们采用非连续伽勒金方法，利用二次有限元在简单三角形上对无摩擦单边接触问题进行有限元逼近。我们首先开发了能量规范中的后验误差估计，并在此基础上讨论了所提出的后验误差估计器的可靠性和效率。离散拉格朗日乘子 𝝀 𝒉 {boldsymbol{lambda_{h}}} 和一些中间算子的适当构造在后验误差分析中起着关键作用。此外，我们还在精确解 𝒖 {boldsymbol{u}} 的适当正则性假设下建立了最优的先验误差估计。 .在均匀网格和自适应网格上给出的数值结果说明并证实了理论结论。

{"title":"Quadratic Discontinuous Galerkin Finite Element Methods for the Unilateral Contact Problem","authors":"Kamana Porwal, Tanvi Wadhawan","doi":"10.1515/cmam-2023-0015","DOIUrl":"https://doi.org/10.1515/cmam-2023-0015","url":null,"abstract":"In this article, we employ discontinuous Galerkin methods for the finite element approximation of the frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We first develop a posteriori error estimates in the energy norm wherein, the reliability and efficiency of the proposed a posteriori error estimator is addressed. The suitable construction of the discrete Lagrange multiplier <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mi>𝝀</m:mi> <m:mi>𝒉</m:mi> </m:msub> </m:math> {boldsymbol{lambda_{h}}} and some intermediate operators play a key role in developing a posteriori error analysis. Further, we establish an optimal a priori error estimates under the appropriate regularity assumption on the exact solution <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>𝒖</m:mi> </m:math> {boldsymbol{u}} . Numerical results presented on uniform and adaptive meshes illustrate and confirm the theoretical findings.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"34 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Computational Methods in Applied Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀