Name
Abstract | ||
|---|---|---|
A new method based on quadratic spline collocation is formulated for the solution of the Dirichlet biharmonic problem on the unit square rewritten as a coupled system of two second-order partial differential equations. This method involves the solution of an auxiliary biharmonic problem using fast Fourier transforms and the solution of a nonsymmetric Schur complement system using preconditioned BICGSTAB, at a total cost of $N^{2} \log N$ on an N × N uniform partition of the unit square. The results of numerical experiments demonstrate the optimality of the global accuracy of the method and also superconvergence results, in particular, third-order accuracy in the $L^{\infty }$ norm of the solution and its fourth-order accuracy at the partition nodes and the collocation points. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1007/s11075-019-00676-z | Numerical Algorithms |
Keywords | Field | DocType |
Biharmonic equation, Quadratic spline collocation, Matrix decomposition algorithms, Fast Fourier transforms, Optimal global convergence rates, Superconvergence | Spline (mathematics),Mathematical analysis,Superconvergence,Unit square,Dirichlet distribution,Biharmonic equation,Collocation method,Mathematics,Schur complement,Collocation | Journal |
Volume | Issue | ISSN |
83 | 1 | 1017-1398 |
Citations | PageRank | References |
1 | 0.40 | 11 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bernard Bialecki | 1 | 114 | 18.61 |
| Graeme Fairweather | 2 | 3 | 1.12 |
| Andreas Karageorghis | 3 | 204 | 47.54 |
| Jonathan Maack | 4 | 1 | 0.73 |