Communications on Applied Mathematics and Computation >

2022 , Vol. 4 >Issue 4: 1374 - 1385

DOI: https://doi.org/10.1007/s42967-021-00180-z

A Mixed Finite-Element Method on Polytopal Mesh

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  • 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 date: 2021-06-08

  Revised date: 2021-12-01

  Online 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.

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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

Cite this article

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 . DOI: 10.1007/s42967-021-00180-z

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