SUPERCONVERGENCE ANALYSIS OF THE POLYNOMIAL PRESERVING RECOVERY FOR ELLIPTIC PROBLEMS WITH ROBIN BOUNDARY CONDITIONS

• 来源期刊: 计算数学（英文版）
• 关键词: Superconvergence Polynomial preserving recovery Finite element methods Robin boundary condition
• 年，卷（期）: 2020,（1）
• 页码范围: 223-238
• 页数: 16页
• 语种: 英文
• DOI: 10.4208/jcm.1911-m2018-0176

摘要

We analyze the superconvergence property of the linear finite element method based on the polynomial preserving recovery (PPR) for Robin boundary elliptic problems on triangulartions.First,we improve the convergence rate between the finite element solution and the linear interpolation under the H1-norm by introducing a class of meshes satisfying the Condition (α,σ,μ).Then we prove the superconvergence of the recovered gradients post-processed by PPR and define an asymptotically exact a posteriori error estimator.Finally,numerical tests are provided to verify the theoretical findings.