Quasi-optimal polytopal finite element methods for biharmonic equation
arXiv:2605.21764
summary
The paper derives quasi‑optimal and lower‑order error bounds for several finite element schemes—including weak Galerkin, discontinuous Galerkin, and hybrid‑high order—applied to the biharmonic equation on general polytopal meshes, and shows that stabilization aids a posteriori error estimation.
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.
Topics & keywords
#finite element methods#biharmonic equation#polytopal meshes#error estimation#weak Galerkin#discontinuous Galerkinquasi-optimal error estimateslower-order error boundsstabilizationa posteriori error estimatorhybrid-high orderpolytopal finite elements