An \(H^ 1\)-Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form
A one-dimensional single-phase Stefan problem is studied both from the theoretical and numerical view point. The problem is first transformed into a quasilinear parabolic equation which is not in divergence form. This parabolic problem is studied through a variational (weak) formulation. Approximation by an \(H^ 1\)-Galerkin procedure is then discussed and optimal error estimates in \(L^ 2\), \(H^ 1\), \(H^ 2\) norms are obtained.
scientific article; zbMATH DE number 4009751