Functional A Posteriori Error Estimates for Maxwell Type Problems
Prof. Dirk PaulyJune 4, 2012, 11:45 a.m. S2 416
This talk is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of boundary value problems for static Maxwell type equations. Our analysis is based upon purely functional argumentation and does not attract specific properties of an approximation method. Therefore, the presented estimates are applicable to any approximate solution which is square integrable. In particular, our results hold for non-conforming approximations.
Such estimates (also called error majorants of functional type) have been derived earlier, e.g., for elliptic problems. We note that generalizations to differential forms are straight forward. Moreover, also the full (time-dependent, hyperbolic) generalized Maxwell system can be treated by similar techniques.