Investigates local convergence of finite element methods for biharmonic problems, indicating new results in derivative approximations.
In this paper, we propose a new approach to investigate the local convergence of finite element approximations for biharmonic problems. We establish new local convergence results for second‐order derivatives in the context of interior penalty finite element approximations. Most significantly, we achieve, for the first time, local convergence results for first‐order derivatives of numerical solutions. Some numerical experiments have been provided to support theoretical findings.
No takes yet. Share an insight, caveat, or question.
He et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: