New Hybridized Mixed Methods for Linear Elasticity and Optimal Multilevel Solvers

2017/04/25 by Shihua Gong, Shuonan Wu, Gong, Shihua +3 · 2 citations
Engineering · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.1704.07540

Abstract

In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions n=2,3, which yields a conforming and strongly symmetric approximation for stress. Applying P_k+1-P_k as the local approximation for the stress and displacement, the mixed methods achieve the optimal order of convergence for both the stress and displacement when k ≥ n. For the lower order case (n-2≤ k

Citations

• Multigrid methods for a parameter dependent problem in primal variables
• Interior Penalty Mixed Finite Element Methods of Any Order in Any Dimension for Linear Elasticity with Strongly Symmetric Stress Tensor

Cited by

• A Least Squares Weak Galerkin Framework for Linear Elasticity on Polytopal Meshes
• A Unified Study of Continuous and Discontinuous Galerkin Methods

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