Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements

DOI10.2478/S11533-012-0159-7zbMath1263.65111OpenAlexW2008821414MaRDI QIDQ1945347

Václav Valenta, Josef Dalík

Publication date: 8 April 2013

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-012-0159-7

zbMATH Keywords

numerical examplesa posteriori error estimatorelliptic boundary-value problemsadaptive solution of elliptic differential problems in 2Daveraging partial derivativeslinear triangular and bilinear rectangular finite elementnonobtuse regular triangulation

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) 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) Numerical differentiation (65D25)

Cites Work

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• Approximations of the partial derivatives by averaging
• Averaging of directional derivatives in vertices of nonobtuse regular triangulations
• Superconvergence phenomenon in the finite element method arising from averaging gradients
• Design sensitivity analysis of structural systems
• How to recover the gradient of linear elements on nonuniform triangulations
• Superconvergence in Galerkin finite element methods
• Superconvergence and Reduced Integration in the Finite Element Method
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• A‐posteriori error estimates for the finite element method

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