Finite element approximation of a model vortex problem. (English) Zbl 0834.65124
The authors study a semilinear elliptic free boundary value problem which arises in the context of inviscid, incompressible fluid dynamics. In particular, they are interested in finite element approximations of solutions of this problem. They show existence of a non trivial, maximal branch of solutions for both the continuous, and for the approximate problem and derive some error estimates.
Reviewer: A.J.Meir (Auburn)
MSC:
65Z05 | Applications to the sciences |
65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
65N15 | Error bounds for boundary value problems involving PDEs |
76B47 | Vortex flows for incompressible inviscid fluids |
76M10 | Finite element methods applied to problems in fluid mechanics |
35J65 | Nonlinear boundary value problems for linear elliptic equations |
35R35 | Free boundary problems for PDEs |
Keywords:
vortex problem; semilinear elliptic free boundary value problem; inviscid, incompressible fluid dynamics; finite element; error estimatesReferences:
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