Error estimates for two-phase stefan problems in several space variables, I: Linear boundary conditions
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- Nochetto, R.H. Calcolo (1985) 22: 457. doi:10.1007/BF02575898
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The enthalpy formulation of two-phase Stefan problems, with linear boundary conditions, is approximated by C0-piecewise linear finite elements in space and backward-differences in time combined with a regularization procedure. Error estimates of L2-type are obtained. For general regularized problems an order ε1/2 is proved, while the order is shown to be ε for non-degenerate cases. For discrete problems an order h2ε−1+h+τε−1/2+τ2/3 is obtained. These orders impose the relations ε∼τ∼h4/3 for the general case and ε∼h∼τ2/3 for non-degenerate problems, in order to obtain rates of convergence h2/3 or h respectively. Besides, an order h|log h|+τ1/2 is shown for finite element meshes with certain approximation property. Also continuous dependence of discrete solutions upon the data is proved.