Penalty-free any-order weak Galerkin FEMs for linear elasticity on quadrilateral meshes. (English) Zbl 1516.65142
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 \(k \ge 0\) 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.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65Y99 | Computer aspects of numerical algorithms |
| 74B05 | Classical linear elasticity |
| 74G15 | Numerical approximation of solutions of equilibrium problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Software:
DarcyLiteReferences:
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