Bank, Randolph E.; Sherman, Andrew H. The use of adaptive grid refinement for badly behaved elliptic partial differential equations. (English) Zbl 0434.35008 Math. Comput. Simulation 22, 18-24 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents MSC: 35A20 Analyticity in context of PDEs 35A25 Other special methods applied to PDEs 35J15 Second-order elliptic equations Keywords:adaptive grid refinement; badly behaved elliptic partial differential equations; singularities; matrix equations Software:YSMP PDFBibTeX XMLCite \textit{R. E. Bank} and \textit{A. H. Sherman}, Math. Comput. Simul. 22, 18--24 (1980; Zbl 0434.35008) Full Text: DOI References: [1] Babuška, I.; Rheinboldt, W. C., Error Estimates for Adaptive Finite Element Computations, SIAM J. Numer. Anal., 15, 736-754 (1978) · Zbl 0398.65069 [2] Babuška, I.; Rheinboldt, W. C., Analysis of Optimal Finite Element Meshes in \(R^1\), (Technical Note BN-869 (March, 1978), Institute for Physical Science and Technology, University of Maryland) · Zbl 0431.65055 [3] Bakhvalov, N. S., On the Convergence of a Relaxation Method with Natural Constraints on the Elliptic Operator, Zh. Vychisl. Mat. mat., 6, 861-885 (1966) · Zbl 0154.41002 [4] Bank, R. E.; Dupont, T., An Optimal Order Process for Solving Finite Element Equations (January 1978), revised [5] Brandt, A., Multi-level Adaptive Solutions to Boundary Value Problems, Math. of Comp., 31, 333-390 (1977) · Zbl 0373.65054 [6] Grimes, R. G.; Kincaid, D. R.; MacGregor, W. I.; Young, D. M., Adaptive Iterative Algorithms Using Symmetric Sparse Storage, (Report CNA 139 (August, 1978), Center for Numerical Analysis, University of Texas at Austin) [7] Eisenstat, S. C.; Gursky, M. C.; Schultz, M. H.; Sherman, A. H., Yale Sparse Matrix Package I: The Symmetric Codes, (Research Report #112 (1977), Department of Computer Science, Yale University) · Zbl 0492.65012 [8] Hackbusch, W., On the Convergence of a Multi-grid Iteration Applied to Finite Element Equations, (Technical Report #77-78 (July, 1977), Universitat Zu Köln) · Zbl 0391.65045 [9] Nicolaides, R. A., On the \(ℓ^2\) Convergence of an Algorithm for Solving Finite Element Equations, Math. of Comp., 31, 892-906 (1977) · Zbl 0384.65052 [10] Oden, J. T.; Reddy, J. N., An Introduction to the Mathematical Theory of Finite Elements (1976), J. Wiley and Sons · Zbl 0336.35001 [11] Strang, G.; Fix, G., An Analysis of the Finite Element Method (1973), Prentice-Hall · Zbl 0278.65116 [12] Varga, R. S., Matrix Iterative Analysis (1962), Prentice-Hall · Zbl 0133.08602 [13] Young, D., Iterative Solution of Large Linear Systems, ((1971), Academic Press) [14] Bank, R. E.; Sherman, A. H., Algorithmic Aspects of the Multi-level Solution of Finite Element Equations, (Report CNA 144 (October 1978), Center for Numerical Analysis, University of Texas at Austin) · Zbl 0466.65058 [15] Bank, R. E.; Sherman, A. H., A Multi-level Iterative Method for Solving Finite Element Equations, Proceedings of the Fifth SPE Symposium and Reservoir Simulation, 117-126 (1979) [17] Houstis, E. N.; Rice, J. R., A Population of Partial Differential Equations for Evaluating Methods, (Report CSD-TR 263 (1978), Computer Sciences Department, Purdue University) · Zbl 0793.68071 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.