Convergence rates for adaptive finite elements. (English) Zbl 1183.65134
The authors present a combination of two known methods to construct the approximate solution of the Dirichlet problem
\[ -\Delta u=f\quad \text{in }\Omega ;\qquad u=0 \quad \text{on } \partial \Omega, \]
using the finite element method. This method consists in a decomposition of the functions in a sum of a regular part and singular terms. The authors indicate an algorithm to construct the adaptive mesh for this problem. Numerical results of the method are not given.
\[ -\Delta u=f\quad \text{in }\Omega ;\qquad u=0 \quad \text{on } \partial \Omega, \]
using the finite element method. This method consists in a decomposition of the functions in a sum of a regular part and singular terms. The authors indicate an algorithm to construct the adaptive mesh for this problem. Numerical results of the method are not given.
Reviewer: Ivan Secrieru (Chişinău)
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
