Abstract
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.
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