A numerical method for solving elliptic interface problems using Petrov-Galerkin formulation with adaptive refinement
type: Item
instance of: scholarly article
title: A numerical method for solving elliptic interface problems using Petrov-Galerkin formulation with adaptive refinement
zbMATH Open document ID: 1427.65382
DOI: 10.1155/2018/3721258
author: Liqun Wang
author: Songming Hou
author: Liwei Shi
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: Elliptic interface problems have wide applications in engineering and science. Non-body-fitted grid has the advantage of saving the cost of mesh generation. In this paper, we propose a Petrov-Galerkin formulation using non-body-fitted grid for solving elliptic interface problems. In this method, adaptive mesh refinement is employed for cells with large errors. The new mesh still has all triangles being right triangles of the same shape. Numerical experiments show side-by-side comparison that to obtain the same accuracy, our new method has much less overall CPU time compared with the previous method even with some cost on mesh generation.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 7018852
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3721258
OpenAlex ID: W2891208280
cites work: Numerical analysis of blood flow in the heart
cites work: The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
cites work: The immersed interface method using a finite element formulation
cites work: Q3085563
cites work: Partially Penalized Immersed Finite Element Methods For Elliptic Interface Problems
cites work: Three-dimensional immersed finite element methods for electric field simulation in composite materials
cites work: A Trilinear Immersed Finite Element Method for Solving the Electroencephalography Forward Problem
cites work: Numerical method for solving matrix coefficient elliptic equation with sharp-edged interfaces
cites work: An improved non-traditional finite element formulation for solving three-dimensional elliptic interface problems
cites work: A numerical method for solving three-dimensional elliptic interface problems with triple junction points
cites work: High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
cites work: Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
cites work: Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
cites work: A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
cites work: A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces
cites work: A sharp interface finite volume method for elliptic equations on Cartesian grids
cites work: A boundary condition capturing method for Poisson's equation on irregular domains
cites work: Convergence of the ghost fluid method for elliptic equations with interfaces
cites work: A new ghost cell/level set method for moving boundary problems: application to tumor growth
cites work: Gradient recovery for elliptic interface problem. II: Immersed finite element methods
cites work: Q4913879
Wikidata QID: Q129268618
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description: scientific article; zbMATH DE number 7018852