An immersed interface method for a 1D poroelasticity problem with discontinuous coefficients

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 the Incompressible Navier--Stokes Equations with Discontinuous Viscosity Across the Interface

We present an immersed interface method for solving the incompressible Navier– Stokes equations with discontinuous viscosity across the interface and singular forces. The method is based on the augmented strategy proposed by Li, Ito, and Lai [Comput. Fluids, 36 (2007), pp. 622–635] to decouple the jump conditions of the fluid variables through the introduction of two augmented variables. In the...

A New Immersed Interface FEM for Elliptic Problems with Discontinuous Coefficients and Nonlinear Local Own Source

)). ( ( )] [( ξ β ξ u g u x x = = (4) Problems of this type arise when we consider a diffusion equation with nonlinear localized chemical reactions. As a result of the reactions the derivatives are discontinuous across the interfaces (local sites of reactions). Some 2D problems with jump conditions, that depend on the solution on the interface are considered by J. Kandilarov and L. Vulkov [2,3,...

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...

A Comparison of the Extended Finite Element Method with the Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources