A note on immersed interface method for three-dimensional elliptic equations

A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity

This paper presents a new high-order immersed interface method for elliptic equations with imbedded interface of discontinuity. Compared with the original second-order immersed interface method of [R.J. LeVeque, Z. Li. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31 (1994) 1001–25], the new method achieves arbitr...

The algebraic immersed interface and boundary method for elliptic equations with jump conditions

A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initia...

The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources

The authors develop finite difference methods for elliptic equations of the form V. ((x)Vu(x)) + (x)u(x) f(x) in a region in one or two space dimensions. It is assumed that gt is a simple region (e.g., a rectangle) and that a uniform rectangular grid is used. The situation is studied in which there is an irregular surface F of codimension contained in fl across which , a, and f may be discontin...

An Immersed Interface Method for Incompressible Navier-Stokes Equations

A Rothe-immersed Interface Method for an Elliptic-parabolic Interface Problem

INTRODUCTION This paper concerns what we term a parabolic-elliptic interface problem. Two – dimensional problems are investigated in many papers [1-4]. They arise in the study of two-dimensional eddy currents [2], in the quasistationary two-dimensional magnetic fields [1], surface measurements [3], etc. In the present paper we shall concentrate on the following simplified model from the biochem...