Prof. Benjamin Seibold (Temple University): Spatial Manifestations of Order Reduction, and Remedies via Weak Stage Order
Meeting ID: 962 1709 1997
Spatial Manifestations of Order Reduction, and Remedies via Weak Stage Order
Prof. Benjamin Seibold (Temple University)
Order reduction, i.e., the convergence of the solution at a lower rate than the formal order of the chosen time-stepping scheme, is a fundamental challenge in stiff problems. Runge-Kutta schemes with high stage order provide a remedy, but unfortunately high stage order is incompatible with DIRK schemes. We first highlight the spatial manifestations of order reduction in PDE IBVPs. Then we introduce the concept of weak stage order, and (a) demonstrate how it overcomes order reduction in important linear PDE problems; and (b) how high-order DIRK schemes can be constructed that are devoid of order reduction.
Mit freundlichen Grüßen,
Prof. Dr. Andreas Meister (AG AAM)