A Coupling Interface Method for a Nonlinear Parabolic-Elliptic Problem

Authors:
Juri D. Kandilarov
Affiliations:
Faculty of Natural Sciences and Education, University of Rousse, Rousse, Bulgaria 7017
Venue:
Numerical Analysis and Its Applications
Year:
2009

Citing 8
Cited 0

Energy methods for a parabolic-hyperbolic interface problem arising in electromagnetism

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Numerical solution of partial differential equations

Numerical solution of partial differential equations
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources

Journal of Computational Physics
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)

The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
A Finite Difference Method and Analysis for 2D Nonlinear Poisson-Boltzmann Equations

Journal of Scientific Computing
The immersed interface method for two-dimensional heat-diffusion equations with singular own sources

Applied Numerical Mathematics
A coupling interface method for elliptic interface problems

Journal of Computational Physics
A monotone iterative method for numerical solution of diffusion equations with nonlinear localized chemical reactions

NMA'06 Proceedings of the 6th international conference on Numerical methods and applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

A coupling interface method (CIM) on uniform cartesian grid for solving parabolic-elliptic problems is proposed. The domain Ω is divided in two subregions Ω − and Ω + . On Ω − we consider an elliptic equation with nonlinear term and on Ω + - a linear parabolic equation. On the interface Γ the standard transmission conditions are stated: the jumps of the solution and the flux are zero. A method of upper and lower solutions is used to deal with the nonlinearity. Numerical experiments are discussed.