We present an efficient Legendre---Galerkin method and its error analysis for a class of PDEs with non-local boundary conditions. We also present several numerical experiments, including the scattering problem from an open cavity, to demonstrate the accuracy and efficiency of the proposed method.
['Lina Hu', 'Lina Ma', 'Jie Shen']
Efficient Spectral-Galerkin Method and Analysis for Elliptic PDEs with Non-local Boundary Conditions