We consider a hybrid FEM-BEM method to compute approximations of full-space linear elliptic transmission problems. First, we derive a priori and a posteriori error estimates. Then, building on the latter, we present an adaptive algorithm and prove that it converges at optimal rates with respect to the number of mesh elements. Finally, we provide numerical experiments, demonstrating the practical performance of the adaptive algorithm.

翻译：本文考虑一种混合有限元-边界元方法以计算全空间线性椭圆型传输问题的逼近解。首先，我们推导先验误差估计与后验误差估计。随后基于后验误差估计，提出一种自适应算法并证明该算法关于网格单元数目以最优速率收敛。最后，通过数值实验展示该自适应算法的实际性能。