6 citations · 6 across the 4 of their papers we have counts for
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Optimal control using flux potentials: A way to construct bound-preserving finite element schemes for conservation laws
Falko Ruppenthal, Dmitri Kuzmin
To ensure preservation of local or global bounds for numerical solutions of conservation laws, we constrain a baseline finite element discretization using optimization-based (OB) f…
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…
A new perspective on flux and slope limiting in discontinuous Galerkin methods for hyperbolic conservation laws
Dmitri Kuzmin
In this work, we discuss and develop multidimensional limiting techniques for discontinuous Galerkin (DG) discretizations of scalar hyperbolic problems. To ensure that each cell av…
Entropy conservation property and entropy stabilization of high-order continuous Galerkin approximations to scalar conservation laws
Dmitri Kuzmin, Manuel Quezada de Luna
This paper addresses the design of linear and nonlinear stabilization procedures for high-order continuous Galerkin (CG) finite element discretizations of scalar conservation laws.…
Entropy stabilization and property-preserving limiters for discontinuous Galerkin discretizations of nonlinear hyperbolic equations
Dmitri Kuzmin
The methodology proposed in this paper bridges the gap between entropy stable and positivity-preserving discontinuous Galerkin (DG) methods for nonlinear hyperbolic problems. The e…
Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws
Dmitri Kuzmin, Manuel Quezada de Luna
In this work, we modify a continuous Galerkin discretization of a scalar hyperbolic conservation law using new algebraic correction procedures. Discrete entropy conditions are used…