Resumen de Well-balanced Finite Volume schemes: some stability and convergence results

Tomás Chacón Rebollo , Antonio Domínguez Delgado , Enrique Domingo Fernández Nieto

• We report a stability and convergence analysis for some simplified well-balanced Finite Volume solvers of Hyperbolic Systems of Conservation Laws. These are specific solvers, recently introduced, that balance all steady solutions up to second order of accuracy by means of an additional numerical source term. We prove the stability and convergence of some of these solvers for scalar hyperbolic equations under reasonable conditions on the additional term.