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Numerical Implementation of the Fictitious Domain Method for Elliptic Equations

Temirbekov A. N., Wójcik W.

International Journal of Electronics and Telecommunications

2014

Vol. 60, No. 3

219-223

In this paper, we consider an elliptic equation with strongly varying coefficients. Interest in the study of these equations is connected with the fact that this type of equation is obtained when using the fictitious domain method. In this paper, we propose a special method for the numerical solution of elliptic equations with strongly varying coefficients. A theorem is proved for the rate of convergence of the iterative process developed. A computational algorithm and numerical calculations are developed to illustrate the effectiveness of the proposed method.

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.