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The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

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Finite-element analysis of a static fluid–solid interaction problem

Araya, Rodolfa and Barrenechea, Gabriel and Jaillet, Fabrice and Rodriguez, Rodolfo (2011) Finite-element analysis of a static fluid–solid interaction problem. IMA Journal of Numerical Analysis, 31 (3). pp. 886-913. ISSN 0272-4979

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Abstract

This paper deals with a fluid–solid interaction problem inspired by a biomechanical brain model. The problem consists of determining the response to prescribed static forces of an elastic solid containing a barotropic and inviscid fluid at rest. The solid is described by means of displacement variables, whereas displacement potential and pressure are used for the fluid. This approach leads to a well-posed symmetric mixed problem, which is discretized by standard Lagrangian finite elements of arbitrary order for all the variables. Optimal-order error estimates in the H1- and L2-norms are proved for this method. A residual a posteriori error estimator is also proposed, for which efficiency and reliability estimates are proved. Finally, some numerical tests are reported to assess the performance of the method and that of an adaptive scheme based on the error estimator.