Mesh refinement and local inversion of elliptic partial differential equations. (English) Zbl 0346.65048
MSC:
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 35J15 | Second-order elliptic equations |
References:
| [1] | A. Brandt; A. Brandt |
| [2] | Buzbee, B. L.; Golub, G. H.; Nielson, C. W., On direct methods for solving Poisson’s equations, SIAM J. Numer. Anal., 7, 627-656 (1970) · Zbl 0217.52902 |
| [3] | Collatz, L., The Numerical Treatment of Differential Equations (1966), Springer-Verlag: Springer-Verlag New York, Appendix · Zbl 0221.65088 |
| [4] | Hockney, R. W., A Fast Direct Solution of Poisson’s Equation Using Fourier Analysis, J. Assoc. Comput. Mach., 95-113 (1965) · Zbl 0139.10902 |
| [5] | Ortega, J. M.; Rheinbolt, N. C., Iterative Solution of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York · Zbl 0241.65046 |
| [6] | Pereyra, V., Variable Order Variable Step Finite Difference Methods for Nonlinear Boundary Value Problems, (Lecture Notes in Mathematics (1974), Springer-Verlag: Springer-Verlag New York), No. 363 · Zbl 0301.65043 |
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