Convergence of goal-oriented adaptive finite element methods for semilinear problems
In this talk, we will discuss a goal-oriented adaptive method for second order semilinear PDEs. In goal-oriented methods we are concerned with approximating a given quantity of interest, a function
of the weak solution to the PDE. In linear problems, this is accomplished by defining a dual problem or formal adjoint and solving the two problems simultaneously. For the semilinear case, we will
discuss the formation of the linearized and approximate dual problems. We will then review the standard contraction framework and discuss some additional estimates used to show convergence of the
method. Finally, we introduce an appropriate notion of error to derive a strong contraction result.
Tuesday, January 31, 2012
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813