A POSTERIORI ERROR ANALYSIS OF A FULLY-MIXED FINITE ELEMENT METHOD FOR A TWO-DIMENSIONAL FLUID-SOLID INTERACTION PROBLEM

• Published in: Journal of computational mathematics Vol. 33; no. 6; pp. 606 - 641
• Main Authors: Domínguez, Carolina, Gatica, Gabriel N., Meddahi, Salim
• Format: Journal Article
• Language: English
• Published: Chinese Academy of Mathematices and System Sciences (AMSS) Chinese Academy of Sciences 01-11-2015
• ISSN: 0254-9409; 1991-7139
• DOI: 10.4208/jcm.1509-m4492

In this paper we develop an a posteriori error analysis of a fully-mixed finite element method for a fluid-solid interaction problem in 2D. The media are governed by the elas-todynamic and acoustic equations in time-harmonic regime, respectively, the transmission conditions are given by the equilibrium of forces and the equality of the corresponding normal displacements, and the fluid is supposed to occupy an annular region surrounding the solid, so that a Robin boundary condition imitating the behavior of the sommerfeld condition is imposed on its exterior boundary. Dual-mixed approaches are applied in both domains, and the governing equations are employed to eliminate the displacenent a of the solid and the pressure p of the fluid. In addition, since both transmission conditions become essential, they are enforced weakly by means of two suitable lahrange multipliers The unknowns of the solid and the fluid are then approximated by a conforming galerkin scheme defined in terms of PEERS elements in the solid, Raviart-Thomas of lowest order in the fluid, and continuous piecewise linear functions on the boundary, As the main con-tribution of this work, we derive a reliable and efficient residual-based a posteriori error estimator for the aforedescribed coupled problem. Some numerical results confirming the properties of the estimator are also reported.