Analysis of Finite Element Methods and Domain Decomposition Algorithms for a Fluid-Solid Interaction Problem

This paper is concerned with the finite element Galerkin approximations for a fluid-solid interaction model proposed in [X. Feng, P. Lee, and Y. Wei, Appl. Anal, submitted]. Both continuous-time and discrete-time approximations are formulated and analyzed. Optimal order a priori estimates for the er...

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Vydané v:SIAM journal on numerical analysis Ročník 38; číslo 4; s. 1312 - 1336
Hlavný autor: Feng, Xiaobing
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia, PA Society for Industrial and Applied Mathematics 2001
Predmet:
A priori knowledge
Algorithms
Applied mathematics
Approximation
Boundary conditions
Decomposition
Decomposition methods
Error rates
Estimation methods
Exact sciences and technology
Finite element method
Fluid solid interactions
Mathematical functions
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Solids
Error estimation
Continuous
Compatibility condition
Acoustic wave
Decomposition method
Continuous time
Duality
Elastic wave
Boundary condition
Fluid solid
Partial differential equation
Solid
System
Finite element method
Fluid solid interaction
Fluid model
Interaction
Initial value problem
Gronwall lemma
Algorithm
Contact surface
Equation system
Fluid solid interface
Analysis method
Boundary value problem
Optimal solution
Discrete time
A priori estimation
Galerkin method
Compatibility
Domain decomposition
Interface
Finite element
ISSN:0036-1429, 1095-7170
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Popis
Shrnutí:This paper is concerned with the finite element Galerkin approximations for a fluid-solid interaction model proposed in [X. Feng, P. Lee, and Y. Wei, Appl. Anal, submitted]. Both continuous-time and discrete-time approximations are formulated and analyzed. Optimal order a priori estimates for the errors in L∞(H1) and L∞(L2) are derived. The main difficulty for the error estimates is caused by the interface conditions which describe the interaction between a fluid and a solid on their contact surface, and it is overcome by using a boundary duality argument of Douglas and Dupont [Numer. Math., 20 (1973), pp. 213-237] to handle the terms involving the interface conditions. Parallelizable domain decomposition algorithms are also proposed and analyzed for efficiently solving the finite element systems.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142999361529