3 papers
math.NA2026
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…
math.NA2026
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…
math.NA2025
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…