Interior Penalty Mixed Finite Element Methods of Any Order in Any Dimension for Linear Elasticity with Strongly Symmetric Stress Tensor

摘要

We propose two classes of mixed finite elements for linear elasticity of anyorder, with interior penalty for nonconforming symmetric stress approximation.One key point of our method is to introduce some appropriate nonconformingface-bubble spaces based on the local decomposition of discrete symmetrictensors, with which the stability can be easily established. We prove theoptimal error estimate for both displacement and stress by adding an interiorpenalty term. The elements are easy to be implemented thanks to the explicitformulations of its basis functions. Moreover, the methods can be applied toarbitrary simplicial grids for any spatial dimension in a unified fashion.Numerical tests for both 2D and 3D are provided to validate our theoreticalresults.