In this paper we give local error estimates in Sobolev norms for the Galerkin method applied to strongly elliptic pseudodifferential equations on a polygon. By using the K-operator, an operator which averages the values of the Galerkin solution, we construct improved approximations.

翻译：本文针对多边形上的强椭圆伪微分方程，给出了伽辽金方法在索伯列夫范数下的局部误差估计。通过使用K算子——一种对伽辽金解值进行平均的算子，我们构建了改进的近似解。