A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909380112285696 |
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| author | Astuto, Clarissa Boffi, Daniele Russo, Giovanni Zerbinati, Umberto |
| author_facet | Astuto, Clarissa Boffi, Daniele Russo, Giovanni Zerbinati, Umberto |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_04048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions Astuto, Clarissa Boffi, Daniele Russo, Giovanni Zerbinati, Umberto Numerical Analysis Analysis of PDEs 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. |
| title | A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2402.04048 |