All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 3 Next

Displaying 41 – 60 of 128

Showing per page

Error estimates for Galerkin reduced-order models of the semi-discrete wave equation

D. Amsallem, U. Hetmaniuk (2014)

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

Galerkin reduced-order models for the semi-discrete wave equation, that preserve the second-order structure, are studied. Error bounds for the full state variables are derived in the continuous setting (when the whole trajectory is known) and in the discrete setting when the Newmark average-acceleration scheme is used on the second-order semi-discrete equation. When the approximating subspace is constructed using the proper orthogonal decomposition, the error estimates are proportional to the sums...

Finite difference scheme for the Willmore flow of graphs

Tomáš Oberhuber (2007)

Kybernetika

In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in Oberhuber [Obe-2005-2,Obe-2005-1] which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry of the solution. Since it requires higher regularity of the solution, additional...

Finite element solution of a hyperbolic-parabolic problem

Rudolf Hlavička (1994)

Applications of Mathematics

Existence and finite element approximation of a hyperbolic-parabolic problem is studied. The original two-dimensional domain is approximated by a polygonal one (external approximations). The time discretization is obtained using Euler’s backward formula (Rothe’s method). Under certain smoothing assumptions on the data (see (2.6), (2.7)) the existence and uniqueness of the solution and the convergence of Rothe’s functions in the space C ( I ¯ , V ) is proved.

Forced anisotropic mean curvature flow of graphs in relative geometry

Dieu Hung Hoang, Michal Beneš (2014)

Mathematica Bohemica

The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.

Frequency analysis of preconditioned waveform relaxation iterations

Andrzej Augustynowicz, Zdzisław Jackiewicz (1999)

Applicationes Mathematicae

The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...

Full discretization of some reaction diffusion equation with blow up

Geneviève Barro, Benjamin Mampassi, Longin Some, Jean Ntaganda, Ousséni So (2006)

Open Mathematics

This paper aims at the development of numerical schemes for nonlinear reaction diffusion problems with a convection that blows up in a finite time. A full discretization of this problem that preserves the blow - up property is presented as well as a numerical simulation. Efficiency of the method is derived via a numerical comparison with a classical scheme based on the Runge Kutta scheme.

Fully discrete error estimation by the method of lines for a nonlinear parabolic problem

Tomáš Vejchodský (2003)

Applications of Mathematics

A posteriori error estimates for a nonlinear parabolic problem are introduced. A fully discrete scheme is studied. The space discretization is based on a concept of hierarchical finite element basis functions. The time discretization is done using singly implicit Runge-Kutta method (SIRK). The convergence of the effectivity index is proven.

Generalized method of lines for first order partial functional differential equations

W. Czernous (2006)

Annales Polonici Mathematici

Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization...

Grid adjustment based on a posteriori error estimators

Karel Segeth (1993)

Applications of Mathematics

The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

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

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...

Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman, Alexandre Ern (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main...

Currently displaying 41 – 60 of 128