Quasi-optimal polytopal finite element methods for biharmonic equation
arXiv:2605.2176437.7
AI Analysis
Provides theoretical guarantees for existing numerical methods on general polytopal meshes, benefiting computational mathematicians working on high-order PDEs.
The paper proves quasi-optimal error estimates for several polytopal finite element methods for the biharmonic equation under minimal regularity, and shows stabilization efficiency in a posteriori error estimators.
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.