The Gradient Superconvergence of Bilinear Finite Volume Element for Elliptic Problems

2015/06/21 by Tie Zhang, Zhang, Tie, Lixin Tang +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1506.06362

openalex publication_date 2015/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient approximation of the FVE solution has the superconvergence property: max_{P∈ S}|(∇ u-∇u_h)(P)|=O(h²)|ln h|, where ∇u_h(P) denotes the average gradient on elements containing point P and S is the set of optimal stress points composed of the mesh points, the midpoints of edges and elements.

Related

• Superconvergence of Ritz-Galerkin Finite Element Approximations for Second Order Elliptic Problems
• Superconvergence in Finite Element Methods and Meshes That are Locally Symmetric with Respect to a Point
• Superconvergence of the Gradient Approximation for Weak Galerkin Finite Element Methods on Nonuniform Rectangular Partitions
• Superconvergence analysis of partially penalized immersed finite element method
• Superconvergence analysis of FEM and SDFEM on graded meshes for a problem with characteristic layers