A High-Order Residual-Based Viscosity Finite Element Method for the Ideal MHD Equations

Abstract We present a high order, robust, and stable shock-capturing technique for finite element approximations of ideal MHD. The method uses continuous Lagrange polynomials in space explicit Runge-Kutta schemes time. term is based on the residual MHD which tracks shock discontinuity positions, adds sufficient amount viscosity to stabilize them. tested up third order polynomial spaces an expected fourth-order convergence rate obtained smooth problems. Several discontinuous benchmarks such as Orszag-Tang, rotor, Brio-Wu problems are solved one, two, three spacial dimensions. Sharp shocks resolutions obtained.