FINITE-ELEMENT APPROXIMATION OF THE PARABOLIC P-LAPLACIAN

In this paper the authors consider the continuous piecewise linear fin ite element approximation in space of the following problem: Given p i s-an-element-of (1, infinity) and u0; find u such that u(t) = del.(\de lu\p-2delu) + f in OMEGA x (0, T], u = 0 on partial derivativeOMEGA x (0, T], u(x, 0) = u0(x) for-all x is-an-element-of OMEGA, where OMEGA subset-of R(d), d = 1 or 2. The authors analyse the semidiscrete appro ximation and a fully discrete approximation using the backward Euler t ime discretisation, obtaining error bounds which improve on those in t he literature.