Error analysis of an algebraic flux correction scheme for a nonlinear scalar conservation law using SSP-RK2

Abstract

We consider a scalar conservation law with linear and nonlinear flux function on a bounded domain Ω ⊂ ℝ2 with Lipschitz boundary Ω. We discretize the spatial variable with the standard finite element method, where we use a local extremum diminishing flux limiter, which is linearity preserving. For temporal discretization, we use the second order explicit strong stability preserving Runge–Kutta method. It is known that the resulting fully-discrete scheme satisfies the discrete maximum principle. Under the sufficiently regularity of the weak solution and the CFL condition k = O(h2), we derive error estimates in e∞(L2)-norm for the algebraic flux correction scheme. We also present numerical experiments that validate that the fully-discrete scheme satisfies the temporal order of convergence of the fully-discrete scheme that we proved in the theoretical analysis.