An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension
type: Item
instance of: scholarly article
title: An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension
zbMATH Open document ID: 1357.65271
author: Xiaoming Zheng
author: John Lowengrub
published in: Advances in Computational Mathematics
publication date: 2017-01-12T00:00:00Z
review text: The paper describes the interface-fitted mesh generation technique and the piecewise linear finite element method for elliptic problems with a general class of jump conditions across the interface. Almost optimal a priori estimates in both \(H^1\) and \(L^2\) norms are proved in this case for both Dirichlet and Neumann problems. Especially, almost the second-order convergence in the region away from the interface in the \(L^2\) norm is obtained. Besides elliptic problems, the method is applied to the Stokes flow and to a tumour growth problem, where Darcy's equations are solved.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 6674202
zbMATH Keywords: interface-fitted
zbMATH Keywords: adaptive mesh
zbMATH Keywords: free interface problems
zbMATH Keywords: elliptic equations with jump conditions
zbMATH Keywords: level-set method
zbMATH Keywords: Stokes equations
zbMATH Keywords: tumor growth
zbMATH Keywords: surface tension
zbMATH Keywords: curvature
zbMATH Keywords: convergence
zbMATH Keywords: Darcy's equations
reviewed by: Tomas Vejchodsky
MaRDI profile type: Publication
full work available at URL: s10444-016-9460-5
OpenAlex ID: W2313679019
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An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension (DOI)
DOI: 10.1007/S10444-016-9460-5