A posteriori error estimates for nonlinear problems.: Lr(0,T;Lρ(Ω))-error estimates for finite element discretizations of parabolic equations

Using the abstract framework of [9] we analyze a residual a posteriori error estimator for space-time finite element discretizations of quasilinear parabolic pdes. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called theta-scheme, which includes the implicit and explicit Euler methods and the Crank-Nicholson scheme.