An error estimate for viscous approximate solutions of degenerate parabolic equations
Steinar Evje, Kenneth H. Karlsen
Abstract
Relying on recent advances in the theory of entropy solutions for nonlinear (strongly) degenerate parabolic equations, we present a direct proof of an L1 error estimate for viscous approximate solutions of the initial value problem for ∂t w+div (V(x)f(w))= ΔA(w) where V=V(x) is a vector field, f=f(u) is a scalar function, and A'(.) ≥ 0. The viscous approximate solutions are weak solutions of the initial value problem for the uniformly parabolic equation ∂t wε+div (V(x) f(wε)) Δ(A(wε)+εwε), ε>0. The error estimate is of order ε.
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