29 citations · 34 across the 6 of their papers we have counts for
6 papers
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.…
Bound-preserving and entropy-stable algebraic flux correction schemes for the shallow water equations with topography
Hennes Hajduk, Dmitri Kuzmin
A well-designed numerical method for the shallow water equations (SWE) should ensure well-balancedness, nonnegativity of water heights, and entropy stability. For a continuous fini…
Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems
Dmitri Kuzmin, Hennes Hajduk, Andreas Rupp
The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of a nonlinear hyperbolic problem to satisfy releva…
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…