Abstract
In this article we discuss the solution of the Dirichlet problem for a class of elliptic operators by a Lagrange multiplier/fictitious domain method. This approach allows the use of regular grids and therefore of fast specialized solvers for problems on complicated geometries; the resulting saddle-point system can be solved by an Uzawa/conjugate gradient algorithm. The resulting methodology is applied to the solution of some flow problems, including external incompressible viscous flow modelled by Navier-Stokes equations.
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Glowinski, R., Pan, TW. & Periaux, J. A Lagrange multiplier/fictitious domain method for the Dirichlet problem — Generalization to some flow problems. Japan J. Indust. Appl. Math. 12, 87–108 (1995). https://doi.org/10.1007/BF03167383
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DOI: https://doi.org/10.1007/BF03167383