In this paper, we will build a roadmap for the growing literature of high order quadrature-
based entropy stable discontinuous Galerkin (DG) methods, trying to elucidate the …

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

Summation-by-parts (SBP) operators are popular building blocks for systematically
develo** stable and high-order accurate numerical methods for time-dependent …

The paper presents high-order accurate, energy-, and entropy-stable discretizations
constructed from summation-by-parts (SBP) operators. Notably, the discretizations assemble …

The flux reconstruction (FR) method has gained popularity in the research community as it
recovers promising high-order methods through modally filtered correction fields, such as …

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

Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated
volume and facet nodes, known as diagonal-E operators, are attractive for entropy-stable …

High order entropy stable discontinuous Galerkin (DG) methods for nonlinear conservation
laws satisfy an inherent discrete entropy inequality. The construction of such schemes has …

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

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