A Preconditioned Finite Element Method for the p-Laplacian Parabolic Equation

In this paper we propose a method for the discretization of the parabolic p-Laplacian equation. In particular we use alternately either the backward Euler scheme or the Crank-Nicolson scheme for the time-discretization and the first order Finite Element Method for space-discretization as in [7]. To obtain the numerical solution we have to invert a block Toeplitz matrix with Toeplitz blocks. To this aim we use a Conjugate Gradient (CG) algorithm preconditioned by a block circulant matrix with circulant blocks. A Two-Dimensional Discrete Fast Sine-Cosine Transform (2D-DFSCT) is applied to invert the block circulant matrix with circulant blocks. The experimental results show how the application of the preconditioner reduces the iterations of the CG algorithm of about the 56% –75%. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)