Premium
A FE‐BE coupling for a fluid‐structure interaction problem: Hierarchical a posteriori error estimates
Author(s) -
Domínguez Catalina,
Stephan Ernst P.,
Maischak Matthias
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20686
Subject(s) - a priori and a posteriori , mathematics , coupling (piping) , fluid–structure interaction , finite element method , boundary (topology) , partial differential equation , reliability (semiconductor) , boundary value problem , mathematical optimization , mathematical analysis , physics , mechanical engineering , philosophy , power (physics) , epistemology , quantum mechanics , engineering , thermodynamics
In this article, we establish a hierarchical a posteriori error estimate for a coupling of finite elements and boundary elements for a fluid‐structure interaction problem posed in two and three dimensions. These methods combine boundary elements for the exterior fluid and finite elements for the elastic structure. We consider two weak formulations, a nonsymmetric one and a symmetric one, which are both uniquely solvable. We present the reliability and efficiency of the error estimates. For the two dimensional case, we compute local error indicators which allow us to develop an adaptive mesh refinement strategy on triangles. For the three dimensional case, we use hexahedrons as elements. Numerical experiments underline our theoretical results. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012