Balanced norm estimates for rp-Finite Element Methods applied to singularly perturbed fourth order boundary value problems

2023/09/19 by Torsten Linß, Linß, Torsten, Christos Xenophontos +1 · 1 citation
Computer Science · Engineering · Mathematics · #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2309.10387

openalex publication_date 2023/09/19 · openalex created_date 2023/09/21 · openalex updated_date 2026/07/28

Abstract

We establish robust exponential convergence for rp-Finite Element Methods (FEMs) applied to fourth order singularly perturbed boundary value problems, in a balanced norm which is stronger than the usual energy norm associated with the problem. As a corollary, we get robust exponential convergence in the maximum norm. r p FEMs are simply p FEMs with possible repositioning of the (fixed number of) nodes. This is done for a C¹ Galerkin FEM in 1-D, and a C⁰ mixed FEM in 2-D over domains with smooth boundary. In both cases we utilize the Spectral Boundary Layer mesh.

Cited by

• Uniform error analysis of a rectangular Morley finite element method on a Shishkin mesh for a 4th-order singularly perturbed boundary value problem

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