Mixed finite element method and high-order local artificial boundary conditions for exterior problems of elliptic equation Original Research Article

The mixed finite element method is used to solve the exterior elliptic problem with high-order local artificial boundary conditions. New unknowns are introduced to reduce the order of the derivatives to two. This leads to an equivalent mixed variational problem such that the normal finite element can be used and special finite elements are no longer needed on the adjacent layer of the artificial boundary. Error estimates are obtained for some local artificial boundary conditions with prescribed order. Numerical examples are presented and the results demonstrate the effectiveness of this method.