This work reports on the performances of a fully-discrete hp-adaptive entropy stable
discontinuous collocated Galerkin method for the compressible Naiver–Stokes equations …

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 develop a general framework for designing conservative numerical methods based on
summation by parts operators and split forms in space, combined with relaxation Runge …

Provably stable flux reconstruction (FR) schemes are derived for partial differential
equations cast in curvilinear coordinates. Specifically, energy stable flux reconstruction …

Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a
semi-discrete entropy inequality under appropriate boundary conditions. In this work, we …

In this paper, we present an entropy-stable Gauss collocation discontinuous Galerkin (DG)
method on 3D curvilinear meshes for the GLM-MHD equations: the single-fluid magneto …

Abstract Summation-by-Parts Finite Differences (SBP-FD) is an approach for approximation
of differential operators satisfying a discrete analogue of integration by parts analytic …

We present an extension of the summation-by-parts (SBP) framework to tensor-product
spectral-element operators in collapsed coordinates. The proposed approach enables the …

In this work, we propose an extension of telescopic derivative operators for the DGSEM with
Gauss nodes, and we prove that this formulation is equivalent to its usual matrix counterpart …

In this article, discrete variants of several results from vector calculus are studied for classical
finite difference summation by parts operators in two and three space dimensions. It is …