Immersed Finite Element Methods for Elliptic Interface Problems with Non-homogeneous Jump Conditions
نویسندگان
چکیده
Abstract. This paper is to develop immersed finite element (IFE) functions for solving second order elliptic boundary value problems with discontinuous coefficients and non-homogeneous jump conditions. These IFE functions can be formed on meshes independent of interface. Numerical examples demonstrate that these IFE functions have the usual approximation capability expected from polynomials employed. The related IFE methods based on the Galerkin formulation can be considered as natural extensions of those IFE methods in the literature developed for homogeneous jump conditions, and they can optimally solve the interface problems with a nonhomogeneous flux jump condition.
منابع مشابه
Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non–body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the di...
متن کاملThe Immersed Finite Volume Element Method for Some Interface Problems with Nonhomogeneous Jump Conditions
In this paper, an immersed finite volume element (IFVE) method is developed for solving some interface problems with nonhomogeneous jump conditions. Using the source removal technique of nonhomogeneous jump conditions, the new IFVE method is the finite volume element method applied to the equivalent interface problems with homogeneous jump conditions and have properties of the usual finite volu...
متن کاملSuperconvergence of immersed finite element methods for interface problems
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desir...
متن کاملA partially penalty immersed Crouzeix-Raviart finite element method for interface problems
The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matri...
متن کاملThe Explicit Jump Immersed Interface Method: Finite Difference Methods for Pde with Piecewise Smooth Solutions We Dedicate This Work to Helmut Rohrl on the Occasion of His 70th Birthday
Many boundary value problems (BVPs) or initial BVPs have non-smooth solutions, with jumps along lower-dimensional interfaces. The Explicit{Jump Immersed Interface Method (EJIIM) was developed following Li's Fast Iterative IIM (FIIIM), recognizing that the foundation for the eecient solution of many such problems is a good solver for elliptic BVPs. EJIIM generalizes the class of problems for whi...
متن کامل