##### Department of Mathematics,

University of California San Diego

****************************

### Center for Computational Mathematics Seminar

## Sara Pollock

## Convergence of goal-oriented adaptive finite element methods

##### Abstract:

In this talk, we will discuss goal-oriented adaptive methods for second order elliptic PDEs. In particular, we will look at linear nonsymmetric and semilinear problem classes. In goal-oriented methods we are concerned with approximating a given quantity of interest, a function of the weak solution to the PDE. The adaptive algorithm is driven by estimating the error in both the primal and a dual problem, which involves the quantity of interest. We will discuss the formation of an appropriate dual for each type of problem, and how the errors in the primal and dual problems relate to the error in the goal function. Finally, we will look at the contraction framework in each instance and address the appropriate notion of error to show convergence.

### April 24, 2012

### 11:00 AM

### AP&M 2402

****************************