18 citations · 19 across the 6 of their papers we have counts for
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Cell-vertex WENO schemes with shock-capturing quadrature for high-order finite element discretizations of hyperbolic problems
Joshua Vedral, Dmitri Kuzmin
We propose a new kind of localized shock capturing for continuous (CG) and discontinuous Galerkin (DG) discretizations of hyperbolic conservation laws. The underlying framework of…
A structure-preserving Lagrangian discontinuous Galerkin method using flux and slope limiting
Joshua Vedral, Nathaniel Morgan, Dmitri Kuzmin +1
We introduce a Lagrangian nodal discontinuous Galerkin (DG) cell-centered hydrodynamics method for solving multi-dimensional hyperbolic systems. By incorporating an adaptation of Z…
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…
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…
Dissipative WENO stabilization of high-order discontinuous Galerkin methods for hyperbolic problems
Joshua Vedral
We present a new approach to stabilizing high-order Runge-Kutta discontinuous Galerkin (RKDG) schemes using weighted essentially non-oscillatory (WENO) reconstructions in the conte…
Dissipation-based WENO stabilization of high-order finite element methods for scalar conservation laws
Dmitri Kuzmin, Joshua Vedral
We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus…