flux-corrected transport

Locally Discrete Maximum Principle DG finite element method for the transport equation

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B1 L4 R4214

In this talk we propose a Flux Corrected Transport (FCT)-like stabilization suitable for high-order Discontinuous Galerkin (DG) finite element discretizations. As a model problem we consider the multi-dimensional transport equation. The method guarantees that the solution satisfies a local Discrete Maximum Principle (DMP). A solution is said to satisfy a DMP locally if any degree of freedom is bounded with respect to the solution at the previous time step in some defined neighborhood.

Algebraic flux correction for finite element discretizations of hyperbolic conservation laws

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B1 L4 R4214

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.

Manuel Quezada De Luna

Research Scientist, Numerical Mathematics
Dr. Suleyman Ulusoy earned both his Ph.D in Mathematics in 2007 and his Master of Science in Applied Mathematics in 2003 from Georgia Institute of Technology in Atlanta, Georgia, USA. He earned both of his Bachelor’s degrees in Mathematics and Mathematics Education from the Middle East Technical University in Ankara, Turkey in 2000. He did postdocs in University of Oslo and University of Maryland. He is currently a faculty member in American University of Ras Al Khaimah.