Journal ArticleDOI
On finite element approximations to time-dependent problems
G. Fix,Nabil Nassif +1 more
TLDR
Best possible error estimates are proved for spline semi-discrete approximations to dissipative initial value problems and error bounds are established for suitable difference quotients.Abstract:
Best possible error estimates are proved for spline semi-discrete approximations to dissipative initial value problems. Error bounds are also established for suitable difference quotients.read more
Citations
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Journal ArticleDOI
Local Spline Approximation Methods
TL;DR: The construction of explicit polynomial spline approximation operators for real-valued functions defined on intervals or on reasonably behaved sets in higher dimensions are studied and are found which apply to wide classes of functions including continuous or integrable functions.
Journal ArticleDOI
Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations
TL;DR: In this article, the authors derived convergence estimates for certain semidiscrete methods used in the approximation of solutions of initial boundary value problems with homogeneous Dirichlet boundary conditions for parabolic equations.
Journal ArticleDOI
Convergence Estimates for Galerkin Methods for Variable Coefficient Initial Value Problems
Vidar Thomée,Burton Wendroff +1 more
TL;DR: The use of Galerkin's method for the approximate solution of the initial value problem for certain simple equations, where P is a differential operator of order m with respect to x, is analyzed in this article.
Book ChapterDOI
A Dissipative Galerkin Method for the Numerical Solution of First Order Hyperbolic Equations
TL;DR: In this paper, a connection between dissipative finite difference operators and a Galerkin-type method for numerical solution of first order one-dimensional hyperbolic problems is discussed.
References
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Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Book
Lectures on Elliptic Boundary Value Problems
TL;DR: In this article, the authors present an introduction to the theory of higher-order elliptic boundary value problems, and a detailed study of basic problems of the theory, such as the problem of existence and regularity of solutions of higher order elliptic edge value problems.
Journal ArticleDOI
Galerkin Methods for Parabolic Equations
Jim Douglas,Todd F. Dupont +1 more
TL;DR: Galerkin-type methods, both continuous and discrete in time, are considered for approximating solutions of linear and nonlinear parabolic problems and bounds reducing the estimation of the error to questions in approximation theory are derived.