An adaptive coupling method for exterior anisotropic elliptic problems

In this paper, we propose an adaptive coupling method for solving anisotropic elliptic PDEs in unbounded domains. Firstly, the existence and the uniqueness of the solution for the coupling method are proven, and the a priori error estimates in H1-norm and L2-norm that depend on the size of the FEM mesh, the location of the elliptic artificial boundary and the truncation of the infinite series in the artificial boundary integral condition are derived. Secondly, the a posteriori error estimates and the a posteriori error indicator of the coupling method are obtained. Finally, the adaptive coupling method refines the mesh distribution by the arc-length equidistribution principle and the a posteriori error indicator successively. Numerical examples confirm the advantage in accuracy and efficiency for the proposed method.