Quasi-optimal polytopal finite element methods for biharmonic equation

TL;DR

This paper develops quasi-optimal finite element methods for the biharmonic equation on general polytopal meshes, providing error estimates and demonstrating the effectiveness of stabilization in error estimation.

Contribution

It introduces and analyzes quasi-optimal finite element methods for biharmonic equations on polytopal meshes, with minimal regularity assumptions and improved error control.

Findings

Established quasi-optimal error estimates for various finite element methods.

Showed stabilization improves a posteriori error estimators.

Validated methods on general polytopal meshes.

Abstract

This paper establishes quasi-optimal and lower-order error estimates for weak Galerkin, discontinuous Galerkin, and hybrid-high order finite element methods for the biharmonic equation under minimal regularity assumptions on general polytopal meshes. Furthermore, it is shown that the stabilization is an efficient contribution in a~posteriori error estimators.