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Adaptive finite element methods for differential equations
  • E. Süli
  • Mathematics, Computer Science
  • Math. Comput.
  • 2005
Gegenstand des Buches ist die Dual Weighted Residual method (DWR), ein sehr effizientes numerisches Verfahren zur Behandlung einer großen Klasse of variationell formulierten Differentialgleichungen, und das Buch gibt einen sehr guten Überblick über die Technik and the Möglichkeiten der DWR. Expand
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
The hp-version of the discontinuous Galerkin finite element method for second-order partial differential equations with nonnegative characteristic form is considered, and an hp-optimal error bound is derived in the hyperbolic case and in the self-adjoint elliptic case. Expand
Numerical solution of partial differential equations
Numerical solution of PDEs is rich and active field of modern applied mathematics. The steady growth of the subject is stimulated by everincreasing demands from the natural sciences, engineering andExpand
An introduction to numerical analysis
Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. Based on a successful course at OxfordExpand
Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
This work considers the enhancement of accuracy, by means of a simple post-processing technique, for finite element approximations to transient hyperbolic equations, and shows results displaying the sharpness of the estimates. Expand
Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality
We give an overview of recent developments concerning the use of adjoint methods in two areas: the a posteriori error analysis of finite element methods for the numerical solution of partialExpand
The main aim of this paper is to highlight that, when dealing with DG methods for linear hyperbolic equations or advection-dominated equations, it is much more convenient to write the upwindExpand
Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations
SummaryThe Lagrange-Galerkin method is a numerical technique for solving convection — dominated diffusion problems, based on combining a special discretisation of the Lagrangian material derivativeExpand
Numerical Solution of Ordinary Differential Equations
• It is often the case when modeling some phenomena that we know something about the rate of change of the quantity of interest, that is, its derivative. • For example, in Calculus I you probablyExpand
Stabilization mechanisms in discontinuous Galerkin finite element methods
In this paper we propose a new general framework for DG methods which allows to uncover a basic mechanism that ensures suitable stability properties of the methods. We show that such a mechanism isExpand