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The coupling of boundary integral and finite element methods for the bidimensional exterior steady stokes problem
Author(s) -
Sequeira A.,
Nedelec J.C.
Publication year - 1983
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670050124
Subject(s) - mathematics , finite element method , mathematical analysis , integral equation , boundary element method , convergence (economics) , boundary (topology) , domain (mathematical analysis) , coupling (piping) , boundary knot method , method of fundamental solutions , boundary value problem , singular boundary method , physics , mechanical engineering , engineering , economics , thermodynamics , economic growth
In this paper, we represent a new numerical method for solving the steady‐state Stokes equations in an unbounded plane domain. The technique consists in coupling the boundary integral and the finite element methods. An artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior one. The solution in the exterior domain is represented by an integral equation over the artificial boundary. This integral equation is incorporated into a velocitypressure formulation for the interior region, and a finite element method is used to approximate the resulting variational problem. This is studied by means of an abstract framework, well adapted to the model problem, in which convergence results and optimal error estimates are derived. Computer results will be discussed in a forthcoming paper.