2017/04/14 by Bernardo Cockburn, Guosheng Fu, Cockburn, Bernardo +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1704.04512
openalex publication_date 2017/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new tool, which we call M-decompositions, for devising superconvergent hybridizable discontinuous Galerkin (HDG) methods and hybridized-mixed methods for linear elasticity with strongly symmetric approximate stresses on unstructured polygonal/polyhedral meshes. We show that for an HDG method, when its local approximation space admits an M-decomposition, optimal convergence of the approximate stress and superconvergence of an element-by-element postprocessing of the displacement field are obtained. The resulting methods are locking-free. Moreover, we explicitly construct approximation spaces that admit M-decompositions on general polygonal elements. We display numerical results on triangular meshes validating our theoretical findings.