High order methods based on diagonal-norm summation by parts operators can be shown
to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of …

In this study, we propose a virtual element scheme to solve the Darcy problem in three
physical dimensions. The main novelty is that curved elements are naturally handled without …

In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-
dimensional computational grids with curvilinear edge elements. The approximation by …

We propose and validate a novel extension of Hybrid High-Order (HHO) methods to meshes
featuring curved elements. HHO methods are based on discrete unknowns that are broken …

We construct entropy conservative and entropy stable discontinuous Galerkin (DG)
discretizations for time-dependent nonlinear hyperbolic conservation laws on curvilinear …

In this paper, we construct new high‐order numerical integration schemes for tetrahedra,
with positive weights and integration points that are in the interior of the domain. The …

Methodologies are presented that enable the construction of provably linearly stable and
conservative high-order discretizations of partial differential equations in curvilinear …

We present a new class of efficient and robust discontinuous spectral-element methods of
arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular …

We introduce a high-order weight-adjusted discontinuous Galerkin (WADG) scheme for the
numerical solution of three-dimensional (3D) wave propagation problems in anisotropic …

Physics-based simulations provide a path to overcome the lack of observational data
hampering a holistic understanding of earthquake faulting and crustal deformation across …