Analysis of Finite Element Methods and Domain Decomposition Algorithms for a Fluid-Solid Interaction Problem
Copyright policy )Analysis of Finite Element Methods and Domain Decomposition Algorithms for a Fluid-Solid Interaction Problem
This paper is concerned with finite element Galerkin approximations for a fluid-solid interaction model. Both continuous-time and discrete-time approximations are formulated and analyzed, and optimal order a priori estimates for the errors in \(L^\infty(H^1)\) and \(L^\infty(L^2)\) are derived. The main difficulty for the error estimates is caused by interface conditions which describe the interaction between fluid and solid on their contact surface. This difficulty is overcome by using a boundary duality argument of \textit{J. Douglas jun.} and \textit{T. Dupont} [Numer. Math. 20, 213-237 (1973; Zbl 0234.65096)] to handle the terms involving the interface conditions. The author also proposes parallelizable domain decomposition algorithms for efficiently solving the arising finite element systems.
optimal order a priori estimates, finite element Galerkin approximations, Finite element methods applied to problems in solid mechanics, parallelizable domain decomposition algorithms, elastic waves, Hydro- and aero-acoustics, acoustic waves, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), fluid-solid interaction model, interface conditions, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, absorbing boundary condition, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, boundary duality argument, Finite element methods applied to problems in fluid mechanics
optimal order a priori estimates, finite element Galerkin approximations, Finite element methods applied to problems in solid mechanics, parallelizable domain decomposition algorithms, elastic waves, Hydro- and aero-acoustics, acoustic waves, Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.), fluid-solid interaction model, interface conditions, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, absorbing boundary condition, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, boundary duality argument, Finite element methods applied to problems in fluid mechanics
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