scholarly journals Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions

2004 ◽  
Vol 2004 (3) ◽  
pp. 932415 ◽  
Author(s):  
Abdelfatah Bouziani ◽  
Nabil Merazga
Keyword(s):  
Wave Equation ◽  
Time Discretization ◽  
Discretization Method ◽  
Integral Conditions ◽  
Quasilinear Wave Equation

scholarly journals Rothe time-discretization method for a nonlocal problem arising in thermoelasticity

2005 ◽  
Vol 2005 (1) ◽  
pp. 13-28 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Continuous Dependence ◽  
Nonlocal Problem ◽  
Time Discretization ◽  
Boundary Integral ◽  
Time Variable ◽  
Discretization Method ◽  
Integral Conditions ◽  
Rothe Method ◽  
Semidiscrete Approximation ◽  
The Given

We investigate a model parabolic mixed problem with purely boundary integral conditions arising in the context of thermoelasticity. Using the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable, the questions of existence, uniqueness, and continuous dependence upon data of a weak solution are proved. Moreover, we establish convergence and derive an error estimate for a semidiscrete approximation.

Solution of a Wave Equation by a Mixed Finite Element - Fictitious Domain Method

2004 ◽  
Vol 4 (4) ◽  
pp. 431-444 ◽  
Author(s):  
Roland Glowinski ◽  
Serguei Lapin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Finite Difference ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Discretization ◽  
Fictitious Domain ◽  
Fictitious Domain Method ◽  
Linear Waves

AbstractThe main goal of this article is to investigate the capability of fictitious domain methods to simulate the scattering of linear waves by an obstacle whose shape does not fit the mesh. The space-time discretization relies on a combination of a mixed finite element method µa la Raviart-Thomas with a fairly standard finite difference scheme for the time discretization. The numerical results described in the article point to a good performance of the numerical method investigated here.

The Quasilinear Wave Equation for Antiplane Shearing of Nonlinearly Elastic Bodies

2001 ◽  
Vol 171 (1) ◽  
pp. 201-226 ◽  
Author(s):  
Dawn A. Lott ◽  
Stuart S. Antman ◽  
William G. Szymczak
Keyword(s):  
Wave Equation ◽  
Quasilinear Wave Equation ◽  
Elastic Bodies ◽  
Nonlinearly Elastic
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