Penalty-Free Any-Order Weak Galerkin FEMs for Linear Elasticity on Quadrilateral Meshes

This paper develops a family of new weak Galerkin (WG) finite element methods (FEMs) for solving linear elasticity in the primal formulation. For a convex quadrilateral mesh, degree k ≥ 0 vector-valued polynomials are used independently in element interiors and on edges for approximating the displac...

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Bibliographic Details
Published in:Journal of scientific computing 2023-04, Vol.95 (1), p.20, Article 20
Main Authors: Wang, Ruishu, Wang, Zhuoran, Liu, Jiangguo
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Boundary value problems
Computational Mathematics and Numerical Analysis
Displacement
Divergence
Elasticity
Finite element method
Galerkin method
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Polynomials
Quadrilaterals
Theoretical
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Summary:This paper develops a family of new weak Galerkin (WG) finite element methods (FEMs) for solving linear elasticity in the primal formulation. For a convex quadrilateral mesh, degree k ≥ 0 vector-valued polynomials are used independently in element interiors and on edges for approximating the displacement. No penalty or stabilizer is needed for these new methods. The methods are free of Poisson-locking and have optimal order ( k + 1 ) convergence rates in displacement, stress, and dilation (divergence of displacement). Numerical experiments on popular test cases are presented to illustrate the theoretical estimates and demonstrate efficiency of these new solvers. Extension to cuboidal hexahedral meshes is briefly discussed.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02151-3