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Fictitious domain approach for numerical solution of elliptic problems

Myśliński A., Żochowski A.

Control and Cybernetics

2000

Vol. 29, no 1

305-323

In the paper the numerical aspects of the fictitious domain method for elliptic problems are considered. Theoretical results concerning the equivalence of original and embedded domain elliptic problems as well as the convergence of discretization are recalled. The dependence of accuracy of numerical solutions to elliptic problems on the approximation of boundary conditions as well as on the order of shape functions are disscussed. The numerical examples are provided.