# the immersed interface method for elliptic equations with discontinuous coefficients and singular sources

@article{LeVeque1994theII, title={the immersed interface method for elliptic equations with discontinuous coefficients and singular sources}, author={Randall J. LeVeque and Zhilin Li}, journal={SIAM Journal on Numerical Analysis}, year={1994}, volume={31}, pages={1019-1044} }

The authors develop finite difference methods for elliptic equations of the form \[ \nabla \cdot (\beta (x)\nabla u(x)) + \kappa (x)u(x) = f(x)\] in a region $\Omega $ in one or two space dimension...

## 1,449 Citations

### The immersed interface method for two-dimensional heat-diffusion equations with singular own sources

- Mathematics
- 2007

### Finite Element Approximation of an Elliptic Boundary Value Problem with Interface

- MathematicsNAA
- 2008

For elliptic boundary value problem in domain with smooth curvilinear boundary and interface a finite element approximation is constructed. Convergence is proved in Sobolev like spaces $\widetilde…

### A Higher Degree Immersed Finite Element Method Based on a Cauchy Extension for Elliptic Interface Problems

- MathematicsSIAM J. Numer. Anal.
- 2019

This article develops and analyzes a $p$th degree immersed finite element (IFE) method for solving the elliptic interface problems with meshes independent of the coefficient discontinuity in the in...

### A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources

- Mathematics
- 2006

We compare the Immersed Interface Method (IIM) with the Extended Finite Element Method (X-FEM) for elliptic equations with singular sources and discontinuous coefficients. The IIM has been compared…

### Finite element methods and their convergence for elliptic and parabolic interface problems

- Mathematics
- 1998

Abstract. In this paper, we consider the finite element methods for solving second order elliptic and parabolic interface problems in two-dimensional convex polygonal domains. Nearly the same optimal…

### The Immersed Interface Technique for Parabolic Problems with Mixed Boundary Conditions

- MathematicsSIAM J. Numer. Anal.
- 2010

A finite difference scheme is presented for a parabolic problem with mixed boundary conditions. We use an immersed interface technique to discretize the Neumann condition, and we use the…

### An immersed finite element method for anisotropic flow models in porous medium

- Mathematics, Computer ScienceInternational Conference on Information Science and Technology
- 2011

An immersed interface finite element method for a kind of anisotropy diffusion models governed by the elliptic interface problems with discontinuous tensor-coefficients based on linear polynomials on non-interface triangular elements and piecewise linear poylemials on interface triangular elements.

### Immersed Interface Difference Schemes for a Parabolic-Elliptic Interface Problem

- Computer ScienceLSSC
- 2007

Second order immersed interface difference schemes for a parabolic-elliptic interface problem arising in electromagnetism is presented. The numerical method uses uniform Cartesian meshes. The…

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