The direct coupling of local discontinuous Galerkin and natural boundary element method for nonlinear interface problem in R3R3

In this article, we use the direct coupling of local discontinuous Galerkin (LDG) and natural boundary element method (NBEM) to solve a class of three-dimensional interface problem, which involves a nonlinear problem in a bounded domain and a Poisson equation in an unbounded domain. A spherical surface as an artificial boundary is introduced. The coupled discrete primal formulation on a bounded domain is obtained. The well-posedness of the primal formulation is verified. The optimal error order with respect to energy norm is given. Numerical examples are presented to demonstrate the optimal convergent rates.