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 …

Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlapping control volumes. Degrees of …

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) …

Bibliography Page 1 Bibliography [1] Y. Achdou, C. Bernardi, and F. Coquel, A priori and a
posteriori analysis of finite volume dis- cretizations of Darcy’s equations, Numer. Math. 96 (2003) …

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 …

A posteriori error estimation for nonlinear variational problems by duality theory Page 1
Journal of Mathematical Sciences, Vol. 99, No. 1, 2000 A POSTERIORI ERROR ESTIMATION …

In this paper we shall derive a posteriori error estimates in the $ L^ 1$-norm for upwind finite
volume schemes for the discretization of nonlinear conservation laws on unstructured grids …

We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-
dimensional advection-diffusion equations with all combinations of inflow and outflow …

We prove a posteriori error estimates for time discretizations by the discontinuous Galerkin
method dG (q) and the corresponding implicit Runge-Kutta-Radau method IRK-R (q) of …