Superconvergence of discontinuous Petrov-Galerkin approximations in linear elasticity

TL;DR

This paper improves convergence results for the discontinuous Petrov-Galerkin method in linear elasticity, demonstrating superconvergence of displacement through duality and post-processing, supported by numerical experiments.

Contribution

It introduces enhanced convergence analysis and superconvergence results for the DPG method in linear elasticity, utilizing duality and post-processing techniques.

Findings

Higher convergence rates for displacement are achieved.

Superconvergence is proven through theoretical analysis.

Numerical experiments confirm the theoretical results.

Abstract

Existing a priori convergence results of the discontinuous Petrov-Galerkin method to solve the problem of linear elasticity are improved. Using duality arguments, we show that higher convergence rates for the displacement can be obtained. Post-processing techniques are introduced in order to prove superconvergence and numerical experiments {\color{black} confirm} our theory.