Displaying similar documents to “Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting”

Combined finite element -- finite volume method (convergence analysis)

Mária Lukáčová-Medviďová (1997)

Commentationes Mathematicae Universitatis Carolinae

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We present an efficient numerical method for solving viscous compressible fluid flows. The basic idea is to combine finite volume and finite element methods in an appropriate way. Thus nonlinear convective terms are discretized by the finite volume method over a finite volume mesh dual to a triangular grid. Diffusion terms are discretized by the conforming piecewise linear finite element method. In the paper we study theoretical properties of this scheme for the scalar nonlinear convection-diffusion...

Finite element approximations of a glaciology problem

Sum S. Chow, Graham F. Carey, Michael L. Anderson (2004)

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

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In this paper we study a model problem describing the movement of a glacier under Glen’s flow law and investigated by Colinge and Rappaz [Colinge and Rappaz, ESAIM: M2AN 33 (1999) 395–406]. We establish error estimates for finite element approximation using the results of Chow [Chow, SIAM J. Numer. Analysis 29 (1992) 769–780] and Liu and Barrett [Liu and Barrett, SIAM J. Numer. Analysis 33 (1996) 98–106] and give an analysis of the convergence of the successive approximations used in...

Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices

Sören Bartels (2005)

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

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This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable...

A finite element scheme for the evolution of orientational order in fluid membranes

Sören Bartels, Georg Dolzmann, Ricardo H. Nochetto (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in [J.B. Fournier and P. Galatoa, (1997) 1509–1520; N. Uchida, (2002) 040902] which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We...

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...

Finite element analysis of a simplified stochastic Hookean dumbbells model arising from viscoelastic flows

Andrea Bonito, Philippe Clément, Marco Picasso (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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A simplified stochastic Hookean dumbbells model arising from viscoelastic flows is considered, the convective terms being disregarded. A finite element discretization in space is proposed. Existence of the numerical solution is proved for small data, so as error estimates, using an implicit function theorem and regularity results obtained in [Bonito (2006) 381–398] for the solution of the continuous problem. error estimates are also derived. Numerical results with...

Superconvergence estimates of finite element methods for American options

Qun Lin, Tang Liu, Shu Hua Zhang (2009)

Applications of Mathematics

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In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and...