Journal ArticleDOI
A Priori Estimates for Mixed Finite Element Methods for the Wave Equation
TLDR
In this paper, the convergence of a mixed method continuous-time scheme for the hyperbolic problem is reduced to a question of convergence of the associated elliptic problem and stability conditions are derived for a conditionally stable explicit scheme.Abstract:
This paper treats mixed methods for second order hyperbolic equations. The convergence of a mixed method continuous-time scheme for the hyperbolic problem is reduced to a question of convergence of the associated elliptic problem. Stability conditions are also derived for a conditionally stable explicit scheme. Numerical experiments are presented that verify the theoretical rates of convergence and compare two of the discrete schemes discussed.read more
Citations
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Journal ArticleDOI
An H 1 -Galerkin Mixed Finite Element Method for Parabolic Partial Differential Equations
TL;DR: In this article, an H1-Galerkin mixed finite element method is proposed and analyzed for parabolic partial differential equations with nonselfadjoint elliptic parts, and it is shown that the finite element approximations have the same rates of convergence as in the classical mixed method.
Journal ArticleDOI
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Marcus J. Grote,Dominik Schötzau +1 more
TL;DR: Here the error analysis is extended to the fully discrete numerical scheme, when a centered second-order finite difference approximation (“leap-frog” scheme) is used for the time discretization.
Journal ArticleDOI
A Priori Error Estimates for Mixed Finite Element Approximations of the Acoustic Wave Equation
TL;DR: This paper derives optimal {a priori} error estimates for mixed finite element displacement formulations of the acoustic wave equation with primary unknowns are pressure and the gradient of pressure.
Journal ArticleDOI
A priori estimates for mixed finite element approximations of second-order hyperbolic equations with absorbing boundary conditions
TL;DR: In this paper, a priori error estimates for mixed finite element approximations for both displacement and stress for a second-order hyperbolic equation with first-order absorbing boundary conditions are derived.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
Journal ArticleDOI
On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers
TL;DR: In this paper, the authors describe a fitting for hose end fittings that is suitable for use in conjunction with a cross-linked polyethylene hose or pipe, where a body incorporating a nipple adapted for insertion in a pipe end and a clamping ring normally retained on the body and adapted for clamping action about the outer surface of said pipe end is described.
Book ChapterDOI
A mixed finite element method for 2-nd order elliptic problems
P. A. Raviart,J. M. Thomas +1 more
Journal ArticleDOI
Two families of mixed finite elements for second order elliptic problems
TL;DR: In this article, two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces.
Journal ArticleDOI
Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
Ivo Babuška,John E. Osborn +1 more
TL;DR: The notion of a generalized finite element method is introduced and this class of methods is analyzed and their relation to mixed methods is discussed.