Error estimates using the cell discretization method for some parabolic problems

The cell discretization algorithm is used to approximate solutions to parabolic problems with coefficients independent of time. Error estimates are obtained showing general convergence for homogeneous problems. A polynomial implementation of the algorithm is described that can be viewed as a nonconforming extension of the finite element method that can also produce the continuous approximations of an h-p finite element method. Numerical tests that confirm the theoretical estimates are discussed.