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

Handlovičová, A.; Krivá, Z.

Displaying similar documents to “Error estimates for finite volume scheme for Perona--Malik equation.”

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

Similarity:

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...

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

Stefano Berrone (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

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...

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

Similarity:

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

Similarity:

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...

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

Mario Ohlberger (2001)

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

Similarity:

This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation $c_{t} + \nabla \cdot (𝐮 f (c)) - \nabla \cdot (D \nabla c) + λ c = 0$ . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the $L^{1}$ -norm, independent of the diffusion parameter $D$ . The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...

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

Similarity:

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....

Quenching semidiscretizations in time of a nonlocal parabolic problem with Neumann boundary condition.

Boni, Théodore K., Kouakou, Thibaut K. (2009)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

Similarity:

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

Similarity:

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.