A Mixed Finite-Element Method on Polytopal Mesh

Yanping Lin; Xiu Ye; Shangyou Zhang

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^,c

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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.

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Yanping Lin, Xiu Ye, Shangyou Zhang. A Mixed Finite-Element Method on Polytopal Mesh. Communications on Applied Mathematics and Computation, 2022, 4(4): 1374‒1385 https://doi.org/10.1007/s42967-021-00180-z