The local ultraconvergence for high-degree Galerkin finite element methods

DOI10.1016/j.jmaa.2016.08.017zbMath1352.65435OpenAlexW2509314427MaRDI QIDQ321739

Wen-ming He, Jiangman Shen, Jun-Zhi Cui

Publication date: 14 October 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.08.017

zbMATH Keywords

numerical examplesfinite element methodsdisplacementderivative recovery operatorrectangular/triangular meshessecond-order elliptic boundary value problemultraconvergence

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (1)

Maximum-norms error estimates for high-order finite volume schemes over quadrilateral meshes

Cites Work

• The local superconvergence of the trilinear element for the three-dimensional Poisson problem
• The superconvergent patch recovery (SPR) and adaptive finite element refinement
• The ultraconvergence of derivative for bicubic finite element
• Superconvergence in high-order Galerkin finite element methods
• Further results on ultraconvergence derivative recovery for odd-order rectangular finite elements
• An acceleration method for integral equations by using interpolation post-processing
• Error estimates of finite element method about elliptic problems with singular righthand side
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• Interior Maximum Norm Estimates for Finite Element Methods
• Asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes. Part II: The piecewise linear case
• Ultraconvergence of the patch recovery technique II
• Analysis of recovery type a posteriori error estimators for mildly structured grids
• Interior Maximum-Norm Estimates for Finite Element Methods, Part II
• Superconvergence in Finite Element Methods and Meshes That are Locally Symmetric with Respect to a Point
• A New Finite Element Gradient Recovery Method: Superconvergence Property
• ISOLATION OF SINGULARITIES OF THE GREEN'S FUNCTION
• Equivalent Norms for Sobolev Spaces
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