A mixed finite element method on polytopal mesh
Yanping Lin, Xiu Ye, Shangyou Zhang
TL;DR
This paper introduces new stable mixed finite element methods of arbitrary order on polytopal meshes for second order elliptic problems, providing optimal error estimates and super convergence, validated through numerical experiments in 2D and 3D.
Contribution
The paper presents novel mixed finite elements applicable to polytopal meshes with proven stability, optimal error estimates, and super convergence, expanding the applicability of finite element methods.
Findings
Optimal order error estimates for velocity
Super convergence for pressure
Numerical experiments confirm theoretical results
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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Taxonomy
TopicsAdvanced Numerical Methods in Computational Mathematics · Differential Equations and Numerical Methods · Numerical methods for differential equations