2024/09/27 by Pervolianakis, Christos
#65M15 #65M60 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2409.18606
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 L2- norm for the algebraic flux correction scheme in space and in ℓ^∞ in time. 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.