##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Ryan Szypowski

#### UCSD

## Adaptive Finite Element Methods for Nonlinear Elliptic Equations

##### Abstract:

The numerical solution of nonlinear elliptic equations is important in many applications; however, it is a challenging task to develop efficient software to solve general problems. This talk will describe the basic finite element method and develop an adaptive framework based on the SOLVE-ESTIMATE-MARK-REFINE iteration. A theory of convergence for this iteration, which allows the solver to be inexact, will be given as well as a new error estimator. Numerical results will be shown for a model problem arising in computational biochemistry.

### April 19, 2011

### 11:00 AM

### AP&M 2402

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