A priori error estimates for a coupled finite element method and mixed finite element method for a fluid-solid interaction problem |
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Authors: | Feng Xiaobing; Xie Zhenghui |
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Institution: |
1 Department of Mathematics, The University of Tennessee, Knoxville TN 37996, USA 2 Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
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Abstract: | This paper presents a heterogeneous finite element method fora fluidsolid interaction problem. The method, which combinesa standard finite element discretization in the fluid regionand a mixed finite element discretization in the solid region,allows the use of different meshes in fluid and solid regions.Both semi-discrete and fully discrete approximations are formulatedand analysed. Optimal order a priori error estimates in theenergy norm are shown. The main difficulty in the analysis iscaused by the two interface conditions which describe the interactionbetween the fluid and the solid. This is overcome by explicitlybuilding one of the interface conditions into the finite elementspaces. Iterative substructuring algorithms are also proposedfor effectively solving the discrete finite element equations. |
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Keywords: | acoustic and elastic waves fluid solid interaction absorbing boundary condition finite element and mixed finite element methods |
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