Global Superconvergence Estimates of Petrov-Galerkin Methods for Hyperbolic Equations

In this paper, Petrov-Galerkin methods are employed for numerical solutions to hyperbolic partial differential equations, which are important mathematical models with many applications in engineering, such as wave transmission, petroleum reservoir. By virtue of superclose analysis and an interpolation postprocessing technique, the global superconvergence is obtained, which is new even for elliptic partial differential equations.