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

Christine Bernardi; Rüdiger Verfürth

Displaying similar documents to “A posteriori error analysis of the fully discretized time-dependent Stokes equations”

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 new error estimate for a fully finite element discretization scheme for parabolic equations using Crank-Nicolson method

Abdallah Bradji, Jürgen Fuhrmann (2014)

Mathematica Bohemica

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Finite element methods with piecewise polynomial spaces in space for solving the nonstationary heat equation, as a model for parabolic equations are considered. The discretization in time is performed using the Crank-Nicolson method. A new a priori estimate is proved. Thanks to this new a priori estimate, a new error estimate in the discrete norm of $𝒲^{1, \infty} (ℒ^{2})$ is proved. An $ℒ^{\infty} (ℋ^{1})$ -error estimate is also shown. These error estimates are useful since they allow us to get second order time accurate approximations...

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...

Error of the two-step BDF for the incompressible Navier-Stokes problem

Etienne Emmrich (2004)

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

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The incompressible Navier-Stokes problem is discretized in time by the two-step backward differentiation formula. Error estimates are proved under feasible assumptions on the regularity of the exact solution avoiding hardly fulfillable compatibility conditions. Whereas the time-weighted velocity error is of optimal second order, the time-weighted error in the pressure is of first order. Suboptimal estimates are shown for a linearisation. The results cover both the two- and three-dimensional...

Error estimates for finite volume scheme for Perona--Malik equation.

Handlovičová, A., Krivá, Z. (2005)

Acta Mathematica Universitatis Comenianae. New Series

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A posteriori error estimates for a nonconforming finite element discretization of the heat equation

Serge Nicaise, Nadir Soualem (2005)

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

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The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in $ℝ^{d}$ , $d = 2$ or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the...

A posteriori error analysis of Euler-Galerkin approximations to coupled elliptic-parabolic problems

Alexandre Ern, Sébastien Meunier (2009)

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

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We analyze Euler-Galerkin approximations (conforming finite elements in space and implicit Euler in time) to coupled PDE systems in which one dependent variable, say $u$ , is governed by an elliptic equation and the other, say $p$ , by a parabolic-like equation. The underlying application is the poroelasticity system within the quasi-static assumption. Different polynomial orders are used for the $u$ - and $p$ -components to obtain optimally convergent a priori bounds for all the terms in the error...

Lagrangian and moving mesh methods for the convection diffusion equation

Konstantinos Chrysafinos, Noel J. Walkington (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington, (2006) 2478–2499; Chrysafinos and Walkington, (2006) 349–366] and the dependence of various constants upon the diffusion parameter is characterized. Error estimates independent...