THE IMMERSED INTERFACE METHOD USING A FINITE-ELEMENT FORMULATION

A finite element method is proposed for one dimensional interface prob lems involving discontinuities in the coefficients of the differential equations and the derivatives of the solutions. The interfaces do not have to be one of grid points. The idea is to construct basis functio ns which satisfy the interface jump conditions. By constructing an int erpolating function of the solution, we are able to give a rigorous er ror analysis which shows that the approximate solution obtained from t he finite element method is second order accurate in the infinity norm . Numerical examples are also provided to support the method and the t heoretical analysis. Several numerical approaches are also proposed fo r dealing with two dimensional. problems involving interfaces. (C) 199 8 Elsevier Science B.V. and IMACS. All rights reserved.