Numerical Analysis of Parabolic p -Laplacian: Approximation of Trajectories
Ning Ju · SIAM Journal on Numerical Analysis · 2000
The long time numerical approximation of the parabolic p-Laplacian problem with a time-independent forcing term and sufficiently smooth initial data is studied. Convergence and stability results which are uniform for $t\in [0,\infty)$ are established in the L 2 , W 1,p norms for the backward Euler and the Crank--Nicholson schemes with the finite element method (FEM). This result extends the existing uniform convergence results for exponentially contractive semigroups generated by some semilinear systems to nonexponentially contractive semigroups generated by some quasi-linear systems.