Numerical Analysis Seminars: Numerical approximation of Poincaré-Friedrichs constants
27 February 2015 14:00 in CM105
The amplitude of a regular function which vanishes on the boundary of a compact region is controlled (integral square) by a constant times the gradient. The smallest possible value of the constant, allowing this to hold true for all functions in the suitable Sobolev space, is non-zero and it is often called the Poincaré-Friedrichs constant. A similar statement is still valid, if we replace the gradient by the curl operator.
Unfortunately, we cannot estimate numerically guaranteed upper bounds for Poincaré-Friedrichs constants by means of a direct application of the classical Galerkin method. The latter might lead, for example, to variational collapse in the case of the curl operator. In this talk we will examine two methods for overcoming this difficulty.
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