scholarly journals On some time marching schemes for the stabilized finite element approximation of the mixed wave equation

2015 ◽  
Vol 296 ◽  
pp. 295-326 ◽  
Author(s):  
Hector Espinoza ◽  
Ramon Codina ◽  
Santiago Badia
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Stabilized Finite Element ◽  
Mixed Wave ◽  
Time Marching

Finite Element Solution and Dispersion Analysis for the Transient Structural Acoustics Problem

1990 ◽  
Vol 43 (5S) ◽  
pp. S381-S388 ◽  
Author(s):  
N. N. Abboud ◽  
P. M. Pinsky
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Finite Element Approximation ◽  
Dispersion Analysis ◽  
Time Dependent ◽  
Element Approximation ◽  
Element Formulation ◽  
Structural Acoustics ◽  
Boundary Operators

In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. The variational statement of the governing equations is developed from a Hamiltonian approach that is modified for nonconservative systems. The dispersive properties of finite element semidiscretizations of the three dimensional wave equation are examined. This analysis throws light on the performance of the finite element approximation over the entire range of wavenumbers and the effects of the order of interpolation, mass lumping, and direction of wave propagation are considered.

scholarly journals Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem

2020 ◽  
Author(s):  
Ramon Codina ◽  
Laura Moreno
Keyword(s):  
Finite Element ◽  
Flow Problem ◽  
Finite Element Approximation ◽  
Viscoelastic Flow ◽  
Element Approximation ◽  
Element Formulation ◽  
Stabilized Finite Element ◽  
Linearized Problem ◽  
Conformation Tensor ◽  
The Stability

In this paper we present the numerical analysis of a finite element method for a linearized viscoelastic flow problem. In particular, we analyze a linearization of the logarithmic reformulation of the problem, which in particular should be able to produce results for Weissenberg numbers higher than the standard one. In order to be able to use the same interpolation for all the unknowns (velocity, pressure and logarithm of the conformation tensor), we employ a stabilized finite element formulation based on the Variational Multi-Scale concept. The study of the linearized problem already serves to show why the logarithmic reformulation performs better than the standard one for high Weissenberg numbers; this is reflected in the stability and error estimates that we provide in this paper.

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