A new optimally convergent finite element method for the transport equation.
Jay Goaplakrishnan,
(Universidad de Florida, EEUU)
Jueves 27 de mayo 2010
Abstract: The subject of this talk is finite element methods of the
Petrov-Galerkin type. They have different trial and test spaces. While
approximate solutions lie in the trial spaces, the equations are satisfied
weakly up to the test spaces. Asserting a general principle that although
one must choose trial spaces with good approximation properties, one may
pick test spaces solely for stability properties, we will exemplify it by
designing specific novel schemes. The presentation will be largely
focused on our initial studies for the transport equations. But the
potential for applying the technique in greater generality will be conveyed.
(Joint work with Leszek Demkowicz.)