Mean-square accuracy estimates of a projection-difference method for weakly solvable quasilinear parabolic equations (Q610328)

The numerical approximation of weakly solvable parabolic problems in separable Hilbert spaces is discussed. For the space variable, the authors use an approximate projection-difference method while a linear Euler method implicit in the leading part is used to deal with the time component. The main result of the paper establishes coercive mean-square estimates for the approximate solutions. As a consequence, the authors deduce further the convergence of the method together with estimates for the rate of convergence both in time and space variable.