Fully-discrete finite element approximations  for
a fourth-order linear stochastic parabolic equation  
with additive space-time white noise

Georgios T. Kossioris; Georgios E. Zouraris

Displaying similar documents to “Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noise”

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...

Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations.

Yan, Yubin (2005)

International Journal of Mathematics and Mathematical Sciences

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A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation

Ivana Šebestová (2014)

Applications of Mathematics

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We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation...

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...

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....