Name
Title | ||
|---|---|---|
Immersed-Interface Finite-Element Methods for Elliptic Interface Problems with Nonhomogeneous Jump Conditions |
Abstract | ||
|---|---|---|
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 discontinuities across the interface in the solution and flux are removed, and an equivalent elliptic interface problem with homogeneous jump conditions is formulated. Special finite-element basis functions are constructed for nodal points near the interface to satisfy the homogeneous jump conditions. Error analysis and numerical tests are presented to demonstrate that such methods have an optimal convergence rate. These methods are designed as an efficient component of the finite-element level-set methodology for fast simulation of interface dynamics that does not require remeshing. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/060666482 | SIAM J. Numerical Analysis |
Keywords | DocType | Volume |
elliptic interface problems,finite-element level-set methodology,nonhomogeneous jump conditions,level-set representation,interface dynamic,elliptic interface problem,new finite-element method,immersed-interface finite-element method,equivalent elliptic interface problem,immersed-interface finite-element methods,special finite-element basis function,nonhomogeneous jump condition,homogeneous jump condition,finite element method | Journal | 46 |
Issue | ISSN | Citations |
1 | 0036-1429 | 46 |
PageRank | References | Authors |
2.34 | 2 | 3 |