A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces
The authors consider the initial value problem \(u'(t) = F(u(t)), t > 0, u(0) = u_0 \in \mathcal{B},\) where \(F: \mathcal{B} \rightarrow X\) under suitable assumptions, \(X\) and \(B\) are abstract complex Banach spaces and \(\mathcal{B} \subset B\) is an open set. The equation is discretized in time by the backward Euler method and the authors prove a posteriori error estimates for the error between the discrete and the exact solution under verifiable assumptions on the data and the computed approximations.
scientific article; zbMATH DE number 5377095