A Splitting Collocation Method for Elliptic Interface Problems

Abstract

An effective method is proposed for interface problems by combining the domain decomposition method and the collocation method. The main idea is to split the whole domain into two non-overlapped sub-domains and enforce the interface conditions to obtain two sub-problems. Each sub-problem is solved by the collocation method. And a simple iterative algorithm is presented to achieve the jump conditions at the interface. The method provided can be used to solve interface problems with both linear and a special type of non-linear jump conditions. Numerical experiments reveal that our method is fourth-order accurate for interface problems.