On the Discontinuous Galerkin Finite Element Method for Reaction-Diffusion Problems: Error Estimates in Energy and Balanced Norms

2017/05/11 by Helena Zarin, Zarin, Helena, Hans-Goerg Roos +1
Computer Science · Engineering · Mathematics · #65L11 #65L20 #65L60 #65L70 #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.1705.04126

openalex publication_date 2017/05/11 · openalex created_date 2017/05/19 · openalex updated_date 2026/07/28

Abstract

A nonsymmetric discontinuous Galerkin FEM with interior penalties has been applied to one-dimensional singularly perturbed reaction-diffusion problems. Using higher order splines on Shishkin-type layer-adapted meshes and certain graded meshes, robust convergence has been proved in the corresponding energy norm and in a balanced norm. Numerical experiments support theoretical findings.

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