Abstract
Free boundary problems appear in a great variety of physical problems. See for instance 1,2,3 for the mathematical setting of many examples. We shall consider here a model case in which the free boundary is the line (or, more generally, the (n−1) dimensional surface) that splits the domain (say, D) where the solution (say, u) is sought, into D = D+ ∪ D0 so that u>0 in D+ and u ≡ 0 in D0. Many free boundary problems can be reduced to this case. If the free boundary is smooth and u is also smooth separately in each subdomain D0 and D+, then the global regularity of u will depend on the behaviour of u, in D+, near the free boundary: for instance, if u behaves like (d(x))k+α (k integer and nonnegative, 0<α≤1, d(x) = distance of x from the free boundary) then u ∈ Ck+α(D). Assume now that we have got, by means of some discretization process, a sequence of discrete solutions {uh}h which converges to u in the L∞ norm. We set
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References
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© 1985 Springer-Verlag Wien
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Brezzi, F. (1985). Error Estimates in the Approximation of a Free Boundary. In: Del Piero, G., Maceri, F. (eds) Unilateral Problems in Structural Analysis. International Centre for Mechanical Sciences, vol 288. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2632-5_2
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DOI: https://doi.org/10.1007/978-3-7091-2632-5_2
Publisher Name: Springer, Vienna
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