Abstract
The paper presents a new finite-difference method for solving the one-dimensional two-phase Stefan problem. Under assumptions on the data which guarantee the temperature u and the moving boundary s to belong to W21,1(ΩT)∩L∞(0,T;W21(Ω)) and W21(0,T), respectively, we obtain L2-error estimates of order O(h + τh−½) provided the time step τ is chosen such that τ≤ch43 Numerical aspects are discussed.
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