Convergence of a finite element method for scalar conservation laws with boundary conditions in two space dimensions

摘要

In this paper, a finite element method for general scalar conservation laws is analyzed: convergence towards the unique solution is proved for two-dimensional space with initial and boundary conditions, by using a uniqueness theorem for measure valued solutions. The method has some advantages: it is an explicit finite element scheme, which is suitable for computing convection dominated flows and discontinuous solutions for multi-dimensional hyperbolic conservation laws. It is superior to other methods in some techniques which are flexible in dealing with convergence.