Work

A posteriori error estimates for nonconforming discretizations of singularly perturbed biharmonic operators

Year: 2024

Type: article

Abstract: For the pure biharmonic equation and a biharmonic singular perturbation problem, a residual-based error estimator is introduced which applies to many existing nonconforming finite elements. The error estimator involves the local best-approximation error of the finite element function by piecewise polynomial functions of the degree determining the expected approximation order, which need not coincide with the maximal polynomial degree of the element, for example if bubble functions are used. The error estimator is shown to be reliable and locally efficient up to this polynomial best-approximation error and oscillations of the right-hand side.

Source: SMAI Journal of Computational Mathematics

DOI: 10.5802/smai-jcm.115

Authors: Dietmar Gallistl, Shudan Tian

Institutions: Friedrich Schiller University Jena, Xiangtan University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutscher Akademischer Austauschdienst, China Scholarship Council, H2020 European Research Council

Awards: Discretization and adaptive approximation of fully nonlinear equations, G8239394213