Finite difference approximations for some interface problems with variable coefficients
type: Item
instance of: scholarly article
title: Finite difference approximations for some interface problems with variable coefficients
zbMATH Open document ID: 1158.65059
author: Boško S. Jovanović
author: Lubin G. Vulkov
published in: Applied Numerical Mathematics
publication date: 2009-01-30T00:00:00Z
review text: The authors investigate a general elliptic interface problem in two variables, in a rectangular domain, crossed by a curvilinear interface. By a suitable variable change, the problem is transformed into an analogous one with a rectilinear interface. For this new interface problem, a finite difference scheme is proposed. Also, the case of a parabolic initial boundary value problem is considered and two finite difference schemes, one implicit and one explicit, for its numerical solution, are proposed. The interface problems are treated in the sense of distributions. Convergence rate estimates in discret Sobolev norms and some abstract stability results are obtained. To improve the efficiency of the proposed implicit scheme for the initial boundary value problem of parabolic type ( because a discrete elliptic problem has to be solved at every time level), the authors develop in the last section an efficient factorized unconditionally stable finite difference scheme. No numerical illustration are made.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5500865
zbMATH Keywords: elliptic and parabolic interface problems
zbMATH Keywords: weak solution
zbMATH Keywords: Sobolev space
zbMATH Keywords: finite difference methods
zbMATH Keywords: convergence
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: j.apnum.2008.03.020
OpenAlex ID: W2128963482
cites work: Convergence of finite difference method for the parabolic problem with concentrated capacity and variable operator
cites work: Bounds for a class of linear functionals with applications to Hermite interpolation
cites work: Uniform difference schemes for a heat equation with concentrated heat capacity
cites work: Finite element methods and their convergence for elliptic and parabolic interface problems
cites work: Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
cites work: Polynomial Approximation of Functions in Sobolev Spaces
cites work: Quasilinear parabolic systems with dynamical boundary conditions
cites work: Mortar methods with curved interfaces
cites work: Q3470840
cites work: Some new a priori estimates for second-order elliptic and parabolic interface problems
cites work: Q4295375
cites work: Q2724526
cites work: Stability of Solutions of Differential-operator and Operator-difference Equations in the Sense of Perturbation of Operators
cites work: On the strong stability of operator-difference schemes in time-integral norms
cites work: Convergence of a finite difference scheme for the third boundary-value problem
cites work: Q2724527
cites work: On the convergence of finite difference schemes for the heat equation with concentrated capacity
cites work: On the Convergence of Difference Schemes for Hyperbolic Problems with Concentrated Data
cites work: Numerical Analysis and Its Applications
cites work: Energy stability for a class of two-dimensional interface linear parabolic problems
cites work: Q3957879
cites work: Q5832587
cites work: An overview of the immersed interface method and its applications
cites work: Q3094428
cites work: Q4528992
cites work: Optimal Error Estimates for Linear Parabolic Problems with Discontinuous Coefficients
cites work: On the Convergence of Finite Element Method for Second Order Elliptic Interface Problems
cites work: Q5807063
cites work: Iterative Methods for Solving Convection-diffusion Problem
cites work: Q3760934
DOI: 10.1016/J.APNUM.2008.03.020
description: scientific article; zbMATH DE number 5500865