On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods.

Goebbels, St.J.

Displaying similar documents to “On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods.”

A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation

Ivana Šebestová (2014)

Applications of Mathematics

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We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation...

Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology

Roland Glowinski, Jacques Rappaz (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical...

Some features of the nodal recovery of gradients from finite element approximations which produces superconvergence

Whiteman, J. R., Goodsell, G.

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Stabilization methods in relaxed micromagnetism

Stefan A. Funken, Andreas Prohl (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential $u$ and magnetization $𝐦$ . In [C. Carstensen and A. Prohl, Numer. Math. 90 (2001) 65–99], the conforming $P 1 - {(P 0)}^{d}$ -element in $d = 2, 3$ spatial dimensions...