In these notes, we study the Runge Kutta Discontinuous Galerkin method for numericaly
solving nonlinear hyperbolic systems and its extension for convection-dominated problems …

SUPG methods were originally developed for the scalar advection‐diffusion equation and
the incompressible Navier‐Stokes equations. In the last few years successful extensions …

This book is the first volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

This is the second paper in a series in which we construct and analyze a class of TVB (total
variation bounded) discontinuous Galerkin finite element methods for solving conservation …

In this paper we study the two-dimensional version of the Runge-Kutta Local Projection
Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one …

An accessible introduction to the finite element method for solving numeric problems, this
volume offers the keys to an important technique in computational mathematics. Suitable for …

A space-time element method is presented for solving the compressible Euler and Navier-
Stokes equations. The proposed formulation includes the variational equation, predictor …

We design arbitrarily high-order accurate entropy stable schemes for systems of
conservation laws. The schemes, termed TeCNO schemes, are based on two main …

The paper outlines the formulation of a novel algorithm which can be used for the solution of
both compressible and incompressible Navier‐Stokes or Euler equations. Full …