Superconvergent pseudostress-velocity finite element methods for the Oseen and Navier-Stokes equations
Numerical Analysis
2021-07-23 v2 Numerical Analysis
Abstract
We present a priori and superconvergence error estimates of mixed finite element methods for the pseudostress-velocity formulation of the Oseen equation. In particular, we derive superconvergence estimates for the velocity and a priori error estimates under unstructured grids, and obtain superconvergence results for the pseudostress under certain structured grids. A variety of numerical experiments validate the theoretical results and illustrate the effectiveness of the superconvergent recovery-based adaptive mesh refinement. It is also numerically shown that the proposed postprocessing yields apparent superconvergence in a benchmark problem for the incompressible Navier--Stokes equation.
Keywords
Cite
@article{arxiv.2001.02805,
title = {Superconvergent pseudostress-velocity finite element methods for the Oseen and Navier-Stokes equations},
author = {Xi Chen and Yuwen Li},
journal= {arXiv preprint arXiv:2001.02805},
year = {2021}
}