Preconditioning Legendre Spectral Collocation Approximations to Elliptic Problems
| Autor: | Ernest E. Rothman, Seymour V. Parter |
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| Rok vydání: | 1995 |
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| Zdroj: | SIAM Journal on Numerical Analysis. 32:333-385 |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/0732015 |
| Popis: | This work deals with the $H^1 $ condition numbers and the distribution of the $\tilde \beta _{N,M} $-singular values of the preconditioned operators $\{ \tilde \beta _{N,M}^{ - 1} W_{N,M} \hat A_{N,M} \} $. $\hat A_{N,M} $ is the matrix representation of the Legendre spectral collocation discretization of the elliptic operator A defined by $Au: = - \Delta u + a_1 u_x + a_2 u_y + a_0 u$ in $\Omega $ (the unit square) with boundary conditions $u = 0$ on $\Gamma _0 $, $\frac{{\partial u}}{{\partial \nu _A }} = \alpha u$ on $\Gamma _1 $. $\tilde \beta _{N,M} $ is the stiffness matrix associated with the finite element discretization of the positive definite elliptic operator B defined by $Bv: = - \Delta v + b_0 v$ in $\Omega $ with boundary conditions $v = 0$ on $\Gamma _0 $, $\frac{{\partial v}}{{\partial \nu _B }} = \beta v$ on $\Gamma _1 $. The finite element space is either the space of continuous functions which are bilinear on the rectangles determined by the Legendre–Gauss–Lobatto (LGL) points or the s... |
| Databáze: | OpenAIRE |
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