An effective linear scheme to solve nonlinear degenerate parabolic differential equations

AbstractIn this paper, we consider the approximate solution of the following problem. Given ω⊂RN (1 ⪯ N ⪯ 3), find u(x, t) such that ∂tb(u)−Δu+Pe▽u=0, in Qω×(0,T), u=0, on ∑∂ω×(0,T), u(x,0)=u0(x), ∀x∈ω, where the function b(s) is a monotonically increasing function satisfying 0 ⪯ b′ ⪯ ∞ To solve this problem, we introduce a new nonstandard time discretization scheme. We prove stability and convergence results