# zbMATH — the first resource for mathematics

Numerical methods for shape identification problems. (English) Zbl 0876.65048
The problem considered here is to minimize a standard quadratic functional, the optimization parameter being an inclusion in the domain. The authors prove an existence result for $$n=2$$, and then discuss first and second optimality conditions based on the technique of material derivative. The numerical method involves boundary elements, the Lagrange-Newton method and a penalty technique. Some numerical examples are discussed.

##### MSC:
 65K10 Numerical optimization and variational techniques 49K20 Optimality conditions for problems involving partial differential equations 49M15 Newton-type methods 49M30 Other numerical methods in calculus of variations (MSC2010)