Work

Anisotropic finite elements for elliptic problems with singular data

Year: 2016

Type: preprint

Abstract: We study the problem $-Δu = γ$, where $γ$ is a singular measure, with support on a curve or a point. We prove that optimal rates of convergence for the finite element method can be obtained using properly graded meshes. In particular, we consider isotropic graded meshes when $γ$ is a point Dirac delta, and anisotropic graded meshes when $γ$ is a measure supported on a segment. Numerical experiments are shown that verify our results, and lead to interesting observations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1610.00798

Author: Ojea, Ignacio

Institution: Fundación Ciencias Exactas y Naturales

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Consejo Nacional de Investigaciones Científicas y Técnicas

OpenAlex ID: W2529469307

Cites: 11

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Related to: 10