A Mixed Finite-Element Method on Polytopal Mesh

doi:10.1007/s42967-021-00180-z

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4): 1374-1385.doi: 10.1007/s42967-021-00180-z

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A Mixed Finite-Element Method on Polytopal Mesh

Yanping Lin¹, Xiu Ye², Shangyou Zhang³

1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China;
2. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA;
3. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

收稿日期:2021-06-08 修回日期:2021-12-01 出版日期:2022-12-20 发布日期:2022-09-26
通讯作者: Shangyou Zhang,E-mail:szhang@udel.edu;Yanping Lin,E-mail:yanping.lin@polyu.edu.hk;Xiu Ye,E-mail:xxye@ualr.edu E-mail:szhang@udel.edu;yanping.lin@polyu.edu.hk;xxye@ualr.edu
基金资助:
This research was supported in part by the National Science Foundation Grant DMS-1620016. This work was also supported in parts by HKSAR grant Q81Q and JRI of The Hong Kong Polytechnic University.

A Mixed Finite-Element Method on Polytopal Mesh

Yanping Lin¹, Xiu Ye², Shangyou Zhang³

1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China;
2. Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA;
3. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

Received:2021-06-08 Revised:2021-12-01 Online:2022-12-20 Published:2022-09-26
Supported by:
This research was supported in part by the National Science Foundation Grant DMS-1620016. This work was also supported in parts by HKSAR grant Q81Q and JRI of The Hong Kong Polytechnic University.

摘要/Abstract

摘要： In this paper, we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic problem. We establish optimal order error estimates for velocity and super convergence for pressure. Numerical experiments are conducted for our mixed elements of different orders on 2D and 3D spaces that confirm the theory.

关键词: Mixed finite-element methods, Second-order elliptic problem, Polytopal mesh

Abstract: In this paper, we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic problem. We establish optimal order error estimates for velocity and super convergence for pressure. Numerical experiments are conducted for our mixed elements of different orders on 2D and 3D spaces that confirm the theory.

Key words: Mixed finite-element methods, Second-order elliptic problem, Polytopal mesh

中图分类号:

Yanping Lin, Xiu Ye, Shangyou Zhang. A Mixed Finite-Element Method on Polytopal Mesh[J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1374-1385.

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A Mixed Finite-Element Method on Polytopal Mesh

A Mixed Finite-Element Method on Polytopal Mesh

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