Displaying similar documents to “Difference methods for non-linear partial differential equations of the first order”

A comparison of some a posteriori error estimates for fourth order problems

Segeth, Karel

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A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...

Implicit difference methods for nonlinear first order partial functional differential systems

Elżbieta Puźniakowska-Gałuch (2010)

Applicationes Mathematicae

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Initial problems for nonlinear hyperbolic functional differential systems are considered. Classical solutions are approximated by solutions of suitable quasilinear systems of difference functional equations. The numerical methods used are difference schemes which are implicit with respect to the time variable. Theorems on convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability is based on a comparison technique with nonlinear...

Analysis of a time discretization scheme for a nonstandard viscous Cahn–Hilliard system

Pierluigi Colli, Gianni Gilardi, Pavel Krejčí, Paolo Podio-Guidugli, Jürgen Sprekels (2014)

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

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In this paper we propose a time discretization of a system of two parabolic equations describing diffusion-driven atom rearrangement in crystalline matter. The equations express the balances of microforces and microenergy; the two phase fields are the order parameter and the chemical potential. The initial and boundary-value problem for the evolutionary system is known to be well posed. Convergence of the discrete scheme to the solution of the continuous problem is proved by a careful...