Solution of Stefan problems by fully discrete linear schemes.
Angela Handlovičová · 1998
where Ω ⊂ R is a polygonal convex domain with the boundary Γ, T <∞, ν is the outward normal to Γ, the functions f, g, β, k are Lipschitz continuous, β : R → R is nondecreasing and k(s) is a positive definite symmetric d × d-matrix for any s ∈ R. The use of linear approximation schemes for solving these problems from both the theoretical and numerical point of view has been extensively studied. A linear approximation scheme based on the so-called nonlinear Chernoff formula with constant relaxation parameter μ was studied in [1], [12], [14], [8]. Another linear approximation scheme was investigated in [5], [6], [7], [3]. There the authors used an approximation scheme of the type