A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations

Mario Ohlberger

Displaying similar documents to “A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations”

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...

Some abstract error estimates of a finite volume scheme for a nonstationary heat equation on general nonconforming multidimensional spatial meshes

Abdallah Bradji, Jürgen Fuhrmann (2013)

Applications of Mathematics

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A general class of nonconforming meshes has been recently studied for stationary anisotropic heterogeneous diffusion problems, see Eymard et al. (IMA J. Numer. Anal. 30 (2010), 1009–1043). Thanks to the basic ideas developed in the stated reference for stationary problems, we derive a new discretization scheme in order to approximate the nonstationary heat problem. The unknowns of this scheme are the values at the centre of the control volumes, at some internal interfaces, and at the...

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....

Arcangeli's type discrepancy principles for a class of regularization methods using a modified projection scheme.

Nair, M.T., Rajan, M.P. (2001)

Abstract and Applied Analysis

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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 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...

Some new error estimates for finite element methods for second order hyperbolic equations using the Newmark method

Abdallah Bradji, Jürgen Fuhrmann (2014)

Mathematica Bohemica

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We consider a family of conforming finite element schemes with piecewise polynomial space of degree $k$ in space for solving the wave equation, as a model for second order hyperbolic equations. The discretization in time is performed using the Newmark method. A new a priori estimate is proved. Thanks to this new a priori estimate, it is proved that the convergence order of the error is $h^{k} + τ^{2}$ in the discrete norms of $ℒ^{\infty} (0, T; ℋ^{1} (Ω))$ and $𝒲^{1, \infty} (0, T; ℒ^{2} (Ω))$ , where $h$ and $τ$ are the mesh size of the spatial and temporal discretization,...