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On mesh independence and Newton-type methods

Owe Axelsson (1993)

Applications of Mathematics

Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters H and h for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error will be...

On monotone and Schwarz alternating methods for nonlinear elliptic PDEs

Shiu-Hong Lui (2001)

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

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs

Shiu-Hong Lui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On numerical integration of implicit ordinary differential equations

Zdzisław Jackiewicz, Marian Kwapisz (1981)

Aplikace matematiky

In this paper it is shown how the numerical methods for ordinary differential equations can be adapted to implicit ordinary differential equations. The resulting methods are of the same order as the corresponding methods for ordinary differential equations. The convergence theorem is proved and some numerical examples are given.

On strongly stable approximations.

F. Arandiga, V. Caselles (1994)

Revista Matemática de la Universidad Complutense de Madrid

In this paper we prove that the convergence of (T - Tn)Tn-k to zero in operator norm (plus some technical conditions) is a sufficient condition for Tn to be a strongly stable approximation to T, thus extending some previous results existing in the literature.

Currently displaying 21 – 40 of 89