ANALYSIS AND FINITE ELEMENT METHODS FOR A FLUID-SOLID INTERACTION PROBLEM IN ONE DIMENSION

1996 ◽  
Vol 06 (08) ◽  
pp. 1119-1141 ◽  
Author(s):  
CH. MAKRIDAKIS ◽  
F. IHLENBURG ◽  
I. BABUŠKA
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Model Problem ◽  
Type System ◽  
Interaction Model ◽  
One Dimension ◽  
Regularity Properties ◽  
Time Harmonic ◽  
Fluid Solid Interaction ◽  
Interaction Problem

In this paper we study a time-harmonic fluid-solid interaction model problem in one dimension. This is a Helmholtz-type system equipped with boundary and transmission conditions. We show the existence of a unique solution to this problem and study its stability and regularity properties. We analyze the convergence of finite element methods with respect to appropriate energy norms. Computational results are also presented.

scholarly journals Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations

2011 ◽  
Vol 81 (278) ◽  
pp. 623-642 ◽  
Author(s):  
Liuqiang Zhong ◽  
Long Chen ◽  
Shi Shu ◽  
Gabriel Wittum ◽  
Jinchao Xu
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Maxwell Equations ◽  
Time Harmonic ◽  
Convergence And Optimality

scholarly journals A Predictor-Corrector Finite Element Method for Time-Harmonic Maxwell’s Equations in Polygonal Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Boniface Nkemzi ◽  
Jake Léonard Nkeck
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
A Priori ◽  
Electric Boundary Condition ◽  
Polygonal Domains ◽  
Time Harmonic ◽  
Predictor Corrector ◽  
Mesh Refinements

The overall efficiency and accuracy of standard finite element methods may be severely reduced if the solution of the boundary value problem entails singularities. In the particular case of time-harmonic Maxwell’s equations in nonconvex polygonal domains Ω, H1-conforming nodal finite element methods may even fail to converge to the physical solution. In this paper, we present a new nodal finite element adaptation for solving time-harmonic Maxwell’s equations with perfectly conducting electric boundary condition in general polygonal domains. The originality of the present algorithm lies in the use of explicit extraction formulas for the coefficients of the singularities to define an iterative procedure for the improvement of the finite element solutions. A priori error estimates in the energy norm and in the L2 norm show that the new algorithm exhibits the same convergence properties as it is known for problems with regular solutions in the Sobolev space H2Ω2 in convex and nonconvex domains without the use of graded mesh refinements or any other modification of the bilinear form or the finite element spaces. Numerical experiments that validate the theoretical results are presented.

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