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 ⊂ R 2 ${\Omega}\subset {\mathbb{R}}^{2}$ 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 ( h 2 ) $k=\mathcal{O}\left({h}^{2}\right)$ , we derive error estimates in ℓ ∞ ( L 2 )-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.