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Recent results in the approximation of free boundaries. (English) Zbl 0608.65080
Differential equations and their applications, Equadiff 6, Proc. 6th Int. Conf., Brno/Czech. 1985, Lect. Notes Math. 1192, 285-289 (1986).
[For the entire collection see Zbl 0595.00009.]
The paper is a survey of the results obtained by the Pavia school in estimating the error in the free boundaries. Essentially, if one knows 1) the behaviour of the exact solution u near the free boundary, 2) the behaviour of the approximate solution \(u_ h\) near the discrete free boundary and 3) an error estimate for \(u-u_ h\) in \(L^ p\), then one can estimate the error in the free boundaries. If the information 2) is lacking one can still get a (weaker) estimate for the error between the continuous free boundary and a suitably modified discrete free boundary.

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
Zbl 0595.00009
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