2015/07/07 by Shuonan Wu, Shihua Gong, Wu, Shuonan +3 · 3 citations
Engineering · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Elasticity and Material Modeling
paper · pdf · doi:10.48550/arxiv.1507.01752
We propose two classes of mixed finite elements for linear elasticity of any order, with interior penalty for nonconforming symmetric stress approximation. One key point of our method is to introduce some appropriate nonconforming face-bubble spaces based on the local decomposition of discrete symmetric tensors, with which the stability can be easily established. We prove the optimal error estimate for both displacement and stress by adding an interior penalty term. The elements are easy to be implemented thanks to the explicit formulations of its basis functions. Moreover, the methods can be applied to arbitrary simplicial grids for any spatial dimension in a unified fashion. Numerical tests for both 2D and 3D are provided to validate our theoretical results.