Unstructured Space-Time Finite Element Methods for Optimal Control of Parabolic Equations

This work presents and analyzes space-time finite element methods on fully unstructured simplicial meshes for the numerical solution of parabolic optimal control problems. Using Babuška's theorem, we show well-posedness first-order optimality systems a typical model problem with linear state equations, but without constraints. is done both continuous discrete levels. Based these results, derive discretization error estimates. Then consider semilinear arising from Schlögl model. The associated nonlinear system solved by Newton's method, where system, which similar to considered problems, has be at each Newton step. We present various experiments including results adaptive discretizations based residual-type indicators. In last two examples, also problems box constraints imposed control.