Displaying similar documents to “Approximation technics for an unsteady dynamic Koiter shell.”

Stability and convergence of two discrete schemes for a degenerate solutal non-isothermal phase-field model

Francisco Guillén-González, Juan Vicente Gutiérrez-Santacreu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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We analyze two numerical schemes of Euler type in time and finite-element type with ℙ 1 -approximation in space for solving a phase-field model of a binary alloy with thermal properties. This model is written as a highly non-linear parabolic system with three unknowns: phase-field, solute concentration and temperature, where the diffusion for the temperature and solute concentration may degenerate. The first scheme is nonlinear, unconditionally stable and convergent....

Skipping transition conditions in error estimates for finite element discretizations of parabolic equations

Stefano Berrone (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we derive error estimates for the heat equation. The time discretization strategy is based on a -method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time...

Convergence of discontinuous Galerkin approximations of an optimal control problem associated to semilinear parabolic PDE's

Konstantinos Chrysafinos (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A discontinuous Galerkin finite element method for an optimal control problem related to semilinear parabolic PDE's is examined. The schemes under consideration are discontinuous in time but conforming in space. Convergence of discrete schemes of arbitrary order is proven. In addition, the convergence of discontinuous Galerkin approximations of the associated optimality system to the solutions of the continuous optimality system is shown. The proof is based on stability estimates at...

A full discretization of the time-dependent Navier-Stokes equations by a two-grid scheme

Hyam Abboud, Toni Sayah (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We study a two-grid scheme fully discrete in time and space for solving the Navier-Stokes system. In the first step, the fully non-linear problem is discretized in space on a coarse grid with mesh-size and time step In the second step, the problem is discretized in space on a fine grid with mesh-size and the same time step, and linearized around the velocity computed in the first step. The two-grid strategy is motivated by the fact that under suitable assumptions,...

A posteriori error analysis of the fully discretized time-dependent Stokes equations

Christine Bernardi, Rüdiger Verfürth (2004)

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

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The time-dependent Stokes equations in two- or three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.