A quasi-optimal space-time finite element method for parabolic equations

We outline the (potential) advantages of simultaneous space-time discretisations of parabolic evolution equations, and illustrate them with some numerical results. Other than for elliptic equations there is not one obvious variational formulation, and we present several possibilities. They have in common that the bilinear form is not coercive so that one has to resort to minimal residual discretisations, in most cases in a dual norm which leads to a saddle point problem. We present some technical details concerning adaptive mesh refinement, the construction of uniformly bounded Fortin interpolators, and optimal preconditioning. Contatto: marco.verani@polimi.it

Rob Stevenson is professor of Applied Analysis at the University of Amsterdam, The Netherlands. In 1990 he received his PhD from the University of Utrecht. He held positions at the University of Utrecht, the Eindhoven University of Technology, and the Radboud University Nijmegen. He was appointed professor at the University of Amsterdam in 2007. He has served/is serving in the editorial boards of several journals in Numerical Analysis and Computational Mathematics. His research is concerned with the numerical solution of partial differential equations. The main focus of his research is on finite element and wavelet methods, multi-level solvers, least squares discretizations, adaptive methods, and space-time methods.