This article surveys a general approach to error control and adaptive mesh design in
Galerkin finite element methods that is based on duality principles as used in optimal …

Stabilized Methods for Compressible Flows Page 1 J Sci Comput (2010) 43: 343–368 DOI
10.1007/s10915-008-9233-5 Stabilized Methods for Compressible Flows Thomas JR Hughes …

This paper gives a review of integration algorithms for finite dimensional mechanical
systems that are based on discrete variational principles. The variational technique gives a …

In this paper, we present an overview of the evolution of the discontinuous Galerkin methods
since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until …

These Lecture Notes have been compiled from the material presented by the second author
in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH …

Knowing thus the Algorithm of this calculus, which I call Differential Calculus, all differential
equations can be solved by a common method (Gottfried Wilhelm von Leibniz, 1646–1719) …

We derive optimal order a posteriori error estimates for time discretizations by both the
Crank–Nicolson and the Crank–Nicolson–Galerkin methods for linear and nonlinear …

The convergence of a class of continuous Galerkin methods for the nonlinear (cubic)
Schrödinger equation is analyzed in this paper. These methods allow variable temporal …

The finite element method can be viewed as a machine that automates the discretization of
differential equations, taking as input a variational problem, a finite element and a mesh, and …

Variational integrators are a class of discretizations for mechanical systems which are
derived by discretizing Hamilton's principle of stationary action. They are applicable to both …