A Novel Family of Q1−Finite Volume Element Schemes on Quadrilateral Meshes

作     者：Zhou, Yanhui Su, Shuai 

作者机构：School of Mathematics and Systems Science Guangdong Polytechnic Normal University Guangzhou510665 China Beijing Institute for Scientific and Engineering Computing Faculty of Science Beijing University of Technology Beijing100124 China 

出 版 物：《SSRN》 

年 卷 期：2024年

核心收录：

主　　题：Coercive force 

摘      要：A novel family of isoparametric bilinear finite volume element schemes are constructed and analyzed to solve the anisotropic diffusion problems on general convex quadrilateral meshes. These new schemes are obtained by employing a special quadrature rule to approximate the line integrals in classical Q1−finite volume element method. The new quadrature rule is a linear combination of trapezoidal and midpoint rules, and the weights depend on a parameter ωK. The novelty of this work is that, for any fully anisotropic diffusion tensor, we provide some specific ωK to ensure the coercivity result of the proposed schemes on arbitrary parallelogram, quasi-parallelogram, trapezoidal and some general convex quadrilateral meshes. More interesting is that, the parameter ωK can only involves the anisotropic diffusion tensor and the geometry of quadrilateral cell. An optimal H1 error estimate is also proved on quasi-parallelogram meshes. Finally, the theoretical findings are validated by several numerical examples. © 2024, The Authors. All rights reserved.