A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions

2024/02/06 by Clarissa Astuto, Daniele Boffi, Astuto, Clarissa +5 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2402.04048

openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper focuses on the numerical solution of elliptic partial differential equations (PDEs) with Dirichlet and mixed boundary conditions, specifically addressing the challenges arising from irregular domains. Both finite element method (FEM) and finite difference method (FDM), face difficulties in dealing with arbitrary domains. The paper introduces a novel nodal symmetric ghost method based on a variational formulation, which combines the advantages of FEM and FDM. The method employs bilinear finite elements on a structured mesh and provides a detailed implementation description. A rigorous a priori convergence rate analysis is also presented. The convergence rates are validated with many numerical experiments, in both one and two space dimensions.

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