4 papers · 1 filter
An element-based convex limiting framework for continuous Galerkin methods with nonlinear stabilization
Dmitri Kuzmin, Hennes Hajduk, Joshua Vedral
We equip a high-order continuous Galerkin discretization of a general hyperbolic problem with a nonlinear stabilization term and introduce a new methodology for enforcing preservat…
Locally energy-stable finite element schemes for incompressible flow problems: Design and analysis for equal-order interpolations
Hennes Hajduk, Dmitri Kuzmin, Gert Lube +1
We show that finite element discretizations of incompressible flow problems can be designed to ensure preservation/dissipation of kinetic energy not only globally but also locally.…
Analysis of algebraic flux correction for semi-discrete advection problems
Hennes Hajduk, Andreas Rupp, Dmitri Kuzmin
We present stability and error analysis for algebraic flux correction schemes based on monolithic convex limiting. For a continuous finite element discretization of the time-depend…
Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws
Hennes Hajduk
In this work we present a framework for enforcing discrete maximum principles in discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to scalar conserv…