algebraic flux correction

Algebraic flux correction for finite element discretizations of hyperbolic conservation laws

Prof. Dmitri Kuzmin, Applied Mathematics, TU Dortmund University

Feb 3, 14:00 - 15:00

B1 L4 R4214

algebraic flux correction hyperbolic problems stabilization techniques flux-corrected transport

In this talk, we review some recent advances in the analysis and design of algebraic flux correction (AFC) schemes for hyperbolic problems. In contrast to most variational stabilization techniques, AFC approaches modify the standard Galerkin discretization in a way which provably guarantees the validity of discrete maximum principles for scalar conservation laws and invariant domain preservation for hyperbolic systems. The corresponding inequality constraints are enforced by adding diffusive fluxes, and bound-preserving antidiffusive corrections are performed to obtain nonlinear high-order approximations. After introducing the AFC methodology and the underlying theoretical framework in the context of continuous piecewise-linear finite element discretizations, we present some of the limiting techniques that we use in high-resolution AFC schemes. This presentation is based on joint work with Dr. Manuel Quezada de Luna (KAUST) and other collaborators.