Optimal isoparametric finite elements and error estimates for domains involving curved boundaries
SIAM Journal on Numerical Analysis
An optimal order multigrid method for biharmonic, C finite element equations
Numerische Mathematik
Mathematics of Computation
Treatments of discontinuity and bubble functions in the multigrid method
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
The optimal refinement strategy for 3-D simplicial meshes
Computers & Mathematics with Applications
Hi-index | 0.00 |
The reaction-diffusion equation on curved domains Ω is considered. The curved boundary is approximated by using isoparametric finite elements. To be able to apply multigrid methods a sequence of finite element triangulations is constructed, which gives a sequence of domains Ωk, k = 0, 1,..., l, approximating the domain Ω. In the case of problems on domains with nonpolynomial boundaries the corresponding finite element spaces are usually nonnested. Therefore, we have to consider solution methods with nonnested spaces. We define a bijection from one approximating domain to another. On this basis a new intergrid transfer operator is constructed and its stability is proved. A pure isoparametric approach is used for obtaining a nonnested multigrid method. An optimal convergence order in an energy norm for the two-level algorithm is proved.