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Auto-stabilized weak Galerkin methods for elasticity problems
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DOI：10.1016/j.cam.2025.117199.png)
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Abstract
En 中文
This paper presents a weak Galerkin (WG) finite element method for linear elasticity on general polygonal and polyhedral meshes, free from convexity constraints, by leveraging bubble functions as central analytical tools. The proposed method eliminates the need for stabilizers commonly used in traditional WG methods, resulting in a simplified formulation. The method is symmetric, positive definite, and straightforward to implement. Optimal-order error estimates are established for the WG approximations in the discrete H1-norm, assuming sufficient smoothness of the exact solution, and in the standard L2-norm under regularity assumptions for the dual problem. Numerical experiments confirm the efficiency and accuracy of the proposed stabilizer-free WG method.
Keywords:
Weak Galerkin
Finite element methods
Auto-stabilized
Weak strain tensor
Non-convex
Bubble functions
Polytopal meshes
Linear elasticity problems
Journal
J
IF:
2.6
Papers:
336
Citations:
0
