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An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized Navier–Stokes flows

Andrea Manzoni (2014)

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

We present the current Reduced Basis framework for the efficient numerical approximation of parametrized steady Navier–Stokes equations. We have extended the existing setting developed in the last decade (see e.g. [S. Deparis, SIAM J. Numer. Anal. 46 (2008) 2039–2067; A. Quarteroni and G. Rozza, Numer. Methods Partial Differ. Equ. 23 (2007) 923–948; K. Veroy and A.T. Patera, Int. J. Numer. Methods Fluids 47 (2005) 773–788]) to more general affine and nonaffine parametrizations (such as volume-based...

An electromagnetic damping machine: model, analysis and numerics

A. Buffa, Y. Maday, F. Rapetti (2001)

Bollettino dell'Unione Matematica Italiana

In questo lavoro viene considerato il modello bidimensionale completo di sistema elettromagnetico in movimento: le equazioni dei campi elettromagnetici sono accoppiate con quelle della meccanica e il sistema così ottenuto risulta essere non lineare nell'accoppiamento. Vengono analizzate la buona posizione del problema e la regolarità della soluzione continua; si propone inoltre uno schema di discretizzazione di tipo esplicito. Si dimostra la buona posizione e la convergenza della formulazione discreta...

An unconditionally stable parallel difference scheme for telegraph equation.

Borhanifar, A., Abazari, Reza (2009)

Mathematical Problems in Engineering

Analysis of an algorithm for computing electromagnetic Bloch modes using Nedelec spaces.

Dobson, D.C., Pasciak, J.E. (2001)

Computational Methods in Applied Mathematics

Analysis of the $A, V - A - ψ$ potential formulation for the eddy current problem in a bounded domain.

Acevedo, Ramiro, Rodríguez, Rodolfo (2007)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots

Patrick Joly, Sébastien Tordeux (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we derive a complete mathematical analysis of a coupled 1D-2D model for 2D wave propagation in media including thin slots. Our error estimates are illustrated by numerical results.

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Veronica Felli, Alberto Ferrero, Susanna Terracini (2011)

Journal of the European Mathematical Society

Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.