Fully reliable error control for evolutionary problems
For researchers in numerical analysis of time-dependent PDEs, this provides a reliable error control method, though it is an incremental extension of existing functional estimates.
This work applies functional-type a posteriori error estimates to evolutionary problems, demonstrating efficient error control via global minimization on time-slabs and a space-time approach, with numerical tests confirming effectiveness.
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also discuss the numerical properties of these bounds that comply with obtained numerical results. This paper examines two different methods of approximate solution reconstruction for evolutionary models, i.e., a time-marching technique and a space-time approach. The first part of the study presents an algorithm for global minimization of the majorant on each of discretization time-cylinders (time-slabs), the effectiveness of this algorithm is confirmed by extensive numerical tests. In the second part of the publication, the application of functional error estimates is discussed with respect to a space-time approach. It is followed by a set of extensive numerical tests that demonstrate the efficiency of proposed error control method.