Pub Date : 2024-02-27DOI: 10.1142/s0218202524400086
Carla Crucianelli, Juan Pablo Pinasco, Nicolas Saintier
In this paper we study Nash equilibria in auctions from the kinetic theory of active particles point of view. We propose a simple learning rule for agents to update their bidding strategies based on their previous successes and failures, in first-price auctions with two bidders. Then, we formally derive the corresponding kinetic equations which describe the evolution over time of the distribution of agents on the bidding strategies. We show that the stationary solution of the equation corresponds to the symmetric Nash equilibrium of the auction, and we prove the convergence to this stationary solution when time goes to infinity. We also introduce a more general learning rule that only depends on the income of agents, and we apply to both first- and second-price auctions. We show that agents learn the Nash equilibrium in first- and second-price auctions with these rules. We present agent-based simulations of the models, and we discuss several open problems.
{"title":"Kinetic theory of active particles meets auction theory","authors":"Carla Crucianelli, Juan Pablo Pinasco, Nicolas Saintier","doi":"10.1142/s0218202524400086","DOIUrl":"https://doi.org/10.1142/s0218202524400086","url":null,"abstract":"<p>In this paper we study Nash equilibria in auctions from the kinetic theory of active particles point of view. We propose a simple learning rule for agents to update their bidding strategies based on their previous successes and failures, in first-price auctions with two bidders. Then, we formally derive the corresponding kinetic equations which describe the evolution over time of the distribution of agents on the bidding strategies. We show that the stationary solution of the equation corresponds to the symmetric Nash equilibrium of the auction, and we prove the convergence to this stationary solution when time goes to infinity. We also introduce a more general learning rule that only depends on the income of agents, and we apply to both first- and second-price auctions. We show that agents learn the Nash equilibrium in first- and second-price auctions with these rules. We present agent-based simulations of the models, and we discuss several open problems.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-23DOI: 10.1142/s0218202524500246
Giuseppe Cardone, Willi Jager, J. L. Woukeng
We derive, through the deterministic homogenization theory in thin domains, a new model consisting of Hele-Shaw equation with memory coupled with the convective Cahn-Hilliard equation. The obtained system, which models in particular tumor growth, is then analyzed and we prove its well-posedness in dimension 2. To achieve our goal, we develop and use the new concept of sigma-convergence in thin heterogeneous media, and we prove some regularity results for the upscaled model.
{"title":"Derivation and analysis of a nonlocal Hele-Shaw-Cahn-Hilliard system for flow in thin heterogeneous layers","authors":"Giuseppe Cardone, Willi Jager, J. L. Woukeng","doi":"10.1142/s0218202524500246","DOIUrl":"https://doi.org/10.1142/s0218202524500246","url":null,"abstract":"We derive, through the deterministic homogenization theory in thin domains, a new model consisting of Hele-Shaw equation with memory coupled with the convective Cahn-Hilliard equation. The obtained system, which models in particular tumor growth, is then analyzed and we prove its well-posedness in dimension 2. To achieve our goal, we develop and use the new concept of sigma-convergence in thin heterogeneous media, and we prove some regularity results for the upscaled model.","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"21 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140436455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-23DOI: 10.1142/s0218202524500209
U. S. Fjordholm, Ola I. H. Maehlen, Magnus C. Orke
{"title":"The Particle Paths of Hyperbolic Conservation Laws","authors":"U. S. Fjordholm, Ola I. H. Maehlen, Magnus C. Orke","doi":"10.1142/s0218202524500209","DOIUrl":"https://doi.org/10.1142/s0218202524500209","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"29 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140436525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-21DOI: 10.1142/s0218202524500155
Weizhu Bao, Ying Ma, Chushan Wang
We establish optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and typical power-type nonlinearity , where is the density with the wave function and the exponent of the nonlinearity. For the first-order Lie–Trotter time-splitting method, optimal -norm error bound is proved for -potential and , and optimal -norm error bound is obtained for -potential and . For the second-order Strang time-splitting method, optimal -norm error bound is established for -potential and , and optimal -norm error bound is proved for -potential and
{"title":"Optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and nonlinearity","authors":"Weizhu Bao, Ying Ma, Chushan Wang","doi":"10.1142/s0218202524500155","DOIUrl":"https://doi.org/10.1142/s0218202524500155","url":null,"abstract":"<p>We establish optimal error bounds on time-splitting methods for the nonlinear Schrödinger equation with low regularity potential and typical power-type nonlinearity <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>f</mi><mo stretchy=\"false\">(</mo><mi>ρ</mi><mo stretchy=\"false\">)</mo><mo>=</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mi>σ</mi></mrow></msup></math></span><span></span>, where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>ρ</mi><mo>:</mo><mo>=</mo><mo>|</mo><mi>ψ</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span> is the density with <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>ψ</mi></math></span><span></span> the wave function and <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>></mo><mn>0</mn></math></span><span></span> the exponent of the nonlinearity. For the first-order Lie–Trotter time-splitting method, optimal <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span>-norm error bound is proved for <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>></mo><mn>0</mn></math></span><span></span>, and optimal <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span></span>-norm error bound is obtained for <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>W</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>≥</mo><mn>1</mn><mo stretchy=\"false\">/</mo><mn>2</mn></math></span><span></span>. For the second-order Strang time-splitting method, optimal <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span>-norm error bound is established for <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>σ</mi><mo>≥</mo><mn>1</mn></math></span><span></span>, and optimal <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span><span></span>-norm error bound is proved for <span><math altimg=\"eq-00015.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>-potential and <span><math altimg=\"eq-00016.gif\" display","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-21DOI: 10.1142/s0218202524400062
Andrea Bondesan, Giuseppe Toscani, Mattia Zanella
We propose a kinetic model for understanding the link between opinion formation phenomena and epidemic dynamics. The recent pandemic has brought to light that vaccine hesitancy can present different phases and temporal and spatial variations, presumably due to the different social features of individuals. The emergence of patterns in societal reactions permits to design and predict the trends of a pandemic. This suggests that the problem of vaccine hesitancy can be described in mathematical terms, by suitably coupling a kinetic compartmental model for the spreading of an infectious disease with the evolution of the personal opinion of individuals, in the presence of leaders. The resulting model makes it possible to predict the collective compliance with vaccination campaigns as the pandemic evolves and to highlight the best strategy to set up for maximizing the vaccination coverage. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.
{"title":"Kinetic compartmental models driven by opinion dynamics: Vaccine hesitancy and social influence","authors":"Andrea Bondesan, Giuseppe Toscani, Mattia Zanella","doi":"10.1142/s0218202524400062","DOIUrl":"https://doi.org/10.1142/s0218202524400062","url":null,"abstract":"<p>We propose a kinetic model for understanding the link between opinion formation phenomena and epidemic dynamics. The recent pandemic has brought to light that vaccine hesitancy can present different phases and temporal and spatial variations, presumably due to the different social features of individuals. The emergence of patterns in societal reactions permits to design and predict the trends of a pandemic. This suggests that the problem of vaccine hesitancy can be described in mathematical terms, by suitably coupling a kinetic compartmental model for the spreading of an infectious disease with the evolution of the personal opinion of individuals, in the presence of leaders. The resulting model makes it possible to predict the collective compliance with vaccination campaigns as the pandemic evolves and to highlight the best strategy to set up for maximizing the vaccination coverage. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140150787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-16DOI: 10.1142/s0218202524500143
Yuwen Li, Jonathan W. Siegel
We present convergence estimates of two types of greedy algorithms in terms of the entropy numbers of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the entropy numbers of the solution manifold in Banach spaces. This contrasts with the classical analysis based on the Kolmogorov -widths and enables us to obtain direct comparisons between the algorithm error and the entropy numbers, where the multiplicative constants are explicit and simple. The entropy-based convergence estimate is sharp and improves upon the classical width-based analysis of reduced basis methods for elliptic model problems. In the second part, we derive a novel and simple convergence analysis of the classical orthogonal greedy algorithm for nonlinear dictionary approximation using the entropy numbers of the symmetric convex hull of the dictionary. This also improves upon existing results by giving a direct comparison between the algorithm error and the entropy numbers.
我们以底层紧凑集的熵数为基础，提出了两类贪婪算法的收敛性估计。在第一部分中，我们用巴拿赫空间中解流形的熵数来衡量参数 PDE 标准贪婪还原基方法的误差。这与基于 Kolmogorov n 宽的经典分析截然不同，使我们能够直接比较算法误差和熵数，其中的乘法常数是明确而简单的。基于熵的收敛估计非常精确，改进了对椭圆模型问题还原基方法的经典基于宽度的分析。在第二部分中，我们利用字典对称凸壳的熵数，对非线性字典逼近的经典正交贪婪算法进行了新颖而简单的收敛分析。通过直接比较算法误差和熵数，这也改进了现有结果。
{"title":"Entropy-based convergence rates of greedy algorithms","authors":"Yuwen Li, Jonathan W. Siegel","doi":"10.1142/s0218202524500143","DOIUrl":"https://doi.org/10.1142/s0218202524500143","url":null,"abstract":"<p>We present convergence estimates of two types of greedy algorithms in terms of the entropy numbers of underlying compact sets. In the first part, we measure the error of a standard greedy reduced basis method for parametric PDEs by the entropy numbers of the solution manifold in Banach spaces. This contrasts with the classical analysis based on the Kolmogorov <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>n</mi></math></span><span></span>-widths and enables us to obtain direct comparisons between the algorithm error and the entropy numbers, where the multiplicative constants are explicit and simple. The entropy-based convergence estimate is sharp and improves upon the classical width-based analysis of reduced basis methods for elliptic model problems. In the second part, we derive a novel and simple convergence analysis of the classical orthogonal greedy algorithm for nonlinear dictionary approximation using the entropy numbers of the symmetric convex hull of the dictionary. This also improves upon existing results by giving a direct comparison between the algorithm error and the entropy numbers.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"135 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-14DOI: 10.1142/s0218202524500106
Frank Ernesto Alvarez, Jules Guilberteau
The well-posedness of a non-local advection–selection–mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such problem by a regularized sum of weighted Dirac masses whose characteristics solve a suitably defined ODE system. The convergence of the particle method over any finite interval is shown and an explicit rate of convergence is given. Furthermore, we investigate the asymptotic-preserving properties of the method in large times, providing sufficient conditions for it to hold true as well as examples and counter-examples. Finally, we illustrate the method in two cases taken from the literature.
{"title":"A particle method for non-local advection–selection–mutation equations","authors":"Frank Ernesto Alvarez, Jules Guilberteau","doi":"10.1142/s0218202524500106","DOIUrl":"https://doi.org/10.1142/s0218202524500106","url":null,"abstract":"<p>The well-posedness of a non-local advection–selection–mutation problem deriving from adaptive dynamics models is shown for a wide family of initial data. A particle method is then developed, in order to approximate the solution of such problem by a regularized sum of weighted Dirac masses whose characteristics solve a suitably defined ODE system. The convergence of the particle method over any finite interval is shown and an explicit rate of convergence is given. Furthermore, we investigate the asymptotic-preserving properties of the method in large times, providing sufficient conditions for it to hold true as well as examples and counter-examples. Finally, we illustrate the method in two cases taken from the literature.</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-02-09DOI: 10.1142/s0218202524500131
Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas
We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of -convergence. Hereby, we generalize the results of the purely elastic setting [M. G. Mora and S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by -convergence, Calc. Var. Partial Differential Equations18 (2003) 287–305] to a framework of free discontinuity problems. The effective one-dimensional model features a classical elastic bending–torsion energy, but also accounts for the possibility that the limiting rod can be broken apart into several pieces or folded. The latter phenomenon can occur because of the persistence of voids in the limit, or due to their collapsing into a discontinuity of the limiting deformation or its derivative. The main ingredient in the proof is a novel rigidity estimate in varying domains under vanishing curvature regularization, obtained in [M. Friedrich, L. Kreutz and K. Zemas, Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces, preprint (2021), arXiv:2107.10808].
我们通过Γ收敛法推导出了带有材料空隙的三维杆的维度还原极限。在此，我们推广了纯弹性环境下的结果 [M. G. Mora and S. Müller, Derivation of the nonlinear bodies]。G. Mora 和 S. Müller，通过Γ-收敛推导出不可伸长杆的非线性弯曲-扭转理论，Calc.Var.Partial Differential Equations18 (2003) 287-305] 到自由不连续问题的框架。有效的一维模型以经典的弹性弯曲扭转能为特征，但也考虑到了极限杆可能断裂成几块或折叠的可能性。后一种现象的出现可能是由于极限中空隙的持续存在，也可能是由于空隙坍塌成极限变形或其导数的不连续。证明的主要内容是[M. Friedrich, L. Kreut]在[M. Friedrich, L. Kreut]中获得的在曲率正则化消失条件下变化域的新刚度估计。Friedrich, L. Kreutz and K. Zemas, Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces, preprint (2021), arXiv:2107.10808].
{"title":"Derivation of effective theories for thin 3D nonlinearly elastic rods with voids","authors":"Manuel Friedrich, Leonard Kreutz, Konstantinos Zemas","doi":"10.1142/s0218202524500131","DOIUrl":"https://doi.org/10.1142/s0218202524500131","url":null,"abstract":"<p>We derive a dimension-reduction limit for a three-dimensional rod with material voids by means of <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>-convergence. Hereby, we generalize the results of the purely elastic setting [M. G. Mora and S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi></math></span><span></span>-convergence, <i>Calc. Var. Partial Differential Equations</i><b>18</b> (2003) 287–305] to a framework of free discontinuity problems. The effective one-dimensional model features a classical elastic bending–torsion energy, but also accounts for the possibility that the limiting rod can be broken apart into several pieces or folded. The latter phenomenon can occur because of the persistence of voids in the limit, or due to their collapsing into a discontinuity of the limiting deformation or its derivative. The main ingredient in the proof is a novel rigidity estimate in varying domains under vanishing curvature regularization, obtained in [M. Friedrich, L. Kreutz and K. Zemas, Geometric rigidity in variable domains and derivation of linearized models for elastic materials with free surfaces, preprint (2021), arXiv:2107.10808].</p>","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140156538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.1142/s0218202524500192
Alejandro Gárriz, Alexis Leculier, S. Mirrahimi
{"title":"Impact of a unilateral horizontal gene transfer on the evolutionary equilibria of a population","authors":"Alejandro Gárriz, Alexis Leculier, S. Mirrahimi","doi":"10.1142/s0218202524500192","DOIUrl":"https://doi.org/10.1142/s0218202524500192","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.1142/s0218202524500180
Volker John, Xu Li, Christian Merdon, Hongxing Rui
{"title":"Inf-sup stabilized Scott–Vogelius pairs on general shape-regular simplicial grids by Raviart–Thomas enrichment","authors":"Volker John, Xu Li, Christian Merdon, Hongxing Rui","doi":"10.1142/s0218202524500180","DOIUrl":"https://doi.org/10.1142/s0218202524500180","url":null,"abstract":"","PeriodicalId":18311,"journal":{"name":"Mathematical Models and Methods in Applied Sciences","volume":"3 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139525392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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