Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems

TL;DR

This paper analyzes the convergence of a finite volume evolution Galerkin method for multidimensional hyperbolic systems, demonstrating stability, consistency, and convergence to strong solutions for linear and nonlinear equations.

Contribution

It introduces a convergence proof for a finite volume evolution Galerkin method applied to multidimensional hyperbolic conservation laws, including Euler equations.

Findings

Proves stability and consistency of the numerical method.

Establishes convergence to strong solutions on the lifespan.

Validates the method for both linear and nonlinear hyperbolic systems.

Abstract

We study the convergence of a finite volume method based on the method of bicharacteristics for multidimensional hyperbolic conservation laws. In particular, we concentrate on the linear wave equation system and nonlinear Euler equations of gas dynamics. We show the stability and the consistency of the numerical approximations. By means of the generalized Lax equivalence principle we prove the convergence of numerical solutions to the strong solution on the lifespan.