A simple finite element method for linear hyperbolic problems

摘要

In this paper, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. This new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.