Runge–Kutta discontinuous Galerkin methods for convection-dominated problems

B Cockburn, CW Shu - Journal of scientific computing, 2001 - Springer
In this paper, we review the development of the Runge–Kutta discontinuous Galerkin
(RKDG) methods for non-linear convection-dominated problems. These robust and accurate …

Basic error estimates for elliptic problems

PG Ciarlet - 1991 - Elsevier
Introduction 23 1. Abstract minimization problems, variational inequalities and the Lax-
Milgram lemma 24 2. The Sobolev spaces H (Q2) and Green's formulae 30 3. Examples of …

Unified analysis of discontinuous Galerkin methods for elliptic problems

DN Arnold, F Brezzi, B Cockburn, LD Marini - SIAM journal on numerical …, 2002 - SIAM
We provide a framework for the analysis of a large class of discontinuous methods for
second-order elliptic problems. It allows for the understanding and comparison of most of the …

[BOOK][B] Nodal discontinuous Galerkin methods: algorithms, analysis, and applications

JS Hesthaven, T Warburton - 2007 - books.google.com
Mathematicsisplayinganevermoreimportant…-ical sciences, provoking a blurring of
boundaries between scienti? c disciplines and a resurgence of interest in the modern as …

An interior penalty finite element method with discontinuous elements

DN Arnold - SIAM journal on numerical analysis, 1982 - SIAM
A new semidiscrete finite element method for the solution of second order nonlinear
parabolic boundary value problems is formulated and analyzed. The test and trial spaces …

[BOOK][B] Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems

M Fortin, R Glowinski - 2000 - books.google.com
The purpose of this volume is to present the principles of the Augmented Lagrangian
Method, together with numerous applications of this method to the numerical solution of …

[BOOK][B] Finite element methods for incompressible flow problems

V John - 2016 - Springer
Incompressible flow problems appear in many models of physical processes and
applications. Their numerical simulation requires in particular a spatial discretization. Finite …

An elliptic collocation-finite element method with interior penalties

MF Wheeler - SIAM Journal on Numerical Analysis, 1978 - SIAM
Ic(x)l<=al, L’w =q, Page 1 SIAM J. NUMER. ANAL. Vol. 15, No. 1, February lt)78 AN ELLIPTIC
COLLOCATION-FINITE ELEMENT METHOD WITH INTERIOR PENALTIES* MARY FANETI" …

The hybrid high-order method for polytopal meshes

DA Di Pietro, J Droniou - Number 19 in Modeling, Simulation and …, 2020 - Springer
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

[BOOK][B] Scientific Computation

P Joly, A Quarteroni, J Rappaz - 2005 - Springer
Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …