5 citations · 14 across the 6 of their papers we have counts for
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Strongly consistent low-dissipation WENO schemes for finite elements
Joshua Vedral, Andreas Rupp, Dmitri Kuzmin
We propose a way to maintain strong consistency and facilitate error analysis in the context of dissipation-based WENO stabilization for continuous and discontinuous Galerkin discr…
Well-balanced convex limiting for finite element discretizations of steady convection-diffusion-reaction equations
Petr Knobloch, Dmitri Kuzmin, Abhinav Jha
We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains…
Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems
Dmitri Kuzmin, Mária Lukácova-Medvid'ová, Philipp Öffner
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on…
Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods
Andrés M Rueda-Ramírez, Benjamin Bolm, Dmitri Kuzmin +1
We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous Galerkin spectral element methods (DGSEM). The use of Legendre-Gauss-Lobatto (LGL) quadrature endo…
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…
An unfitted finite element method using level set functions for extrapolation into deformable diffuse interfaces
Dmitri Kuzmin, Jan-Phillip Bäcker
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continu…