Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

UCNS3D is an open-source computational solver for compressible flows on unstructured
meshes. State-of-the-art high-order methods and their associated benefits can now be …

In this paper, we investigate the accuracy and efficiency of discontinuous Galerkin spectral
method simulations of under‐resolved transitional and turbulent flows at moderate Reynolds …

A comparison study of the efficiency and accuracy of a variety of meshless trial and test
functions is presented in this paper, based on the general concept of the meshless local …

This paper is concerned with the numerical solution of the unified first order hyperbolic
formulation of continuum mechanics recently proposed by Peshkov and Romenski [110] …

In this paper, we propose a new unified family of arbitrary high order accurate explicit one-
step finite volume and discontinuous Galerkin schemes on unstructured triangular and …

Discontinuous Galerkin (DG) methods are a class of finite element methods using
discontinuous basis functions, which are usually chosen as piecewise polynomials. Since …

We introduce a simple and general framework for the construction of thermodynamically
compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems …

In this paper we develop a family of very high-order central (up to 6th-order) non-oscillatory
schemes for mixed-element unstructured meshes. The schemes are inherently compact in …

A new discontinuous Galerkin finite element method for solving diffusion problems is
introduced. Unlike the traditional local discontinuous Galerkin method, the scheme called …