Preconditioning cubic spline collocation discretization by \(P_1\) finite element method on an irregular mesh. (English) Zbl 0991.65121
Summary: By showing the exponential decay of the cubic interpolatory spline on an irregular mesh, we extend the preconditioning results of S. D. Kim and S. V. Parker [Numer. Math. 72, No. 1, 39-72 (1995; Zbl 0844.65086)] for
\[
Au:= -\Delta u+ (a(x)+ a(y)) u
\]
by the \(P_1\) finite element method on a quasiuniform mesh.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
