An efficient algorithm for stiff elliptic problems with applications to the method of fictitious domains. (English. Russian original) Zbl 0970.65121

Comput. Math. Math. Phys. 39, No. 6, 884-896 (1999); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 6, 919-931 (1999).
Summary: A stiff elliptic boundary value problem with a parameter \(\varepsilon\) at the highest derivative that usually arises in the method of fictitious domains is examined. A finite element approximation and an iterative algorithm for solving this problem are discussed. The convergence rate of the algorithm is shown to be independent of the scatter of coefficients or the discretization parameter.


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations