An $hp$-version error analysis of the discontinuous Galerkin method for linear elasticity
This work provides theoretical error bounds for a numerical method in computational mechanics, but it is an incremental extension of existing techniques to a specific problem.
The authors develop an hp-version error analysis for the discontinuous Galerkin method applied to linear elasticity, providing error estimates in energy and L2 norms, supported by numerical experiments.
An $hp$-version error analysis is developed for the general DG method in mixed formulation for solving the linear elastic problem. First of all, we give the $hp$-version error estimates of two $L^2$ projection operators. Then incorporated with the techniques in [11], we obtain the $hp$-version error estimates in energy norm and $L^2$ norm. Some numerical experiments are provided for demonstrating the theoretical results.