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The use of adaptive grid refinement for badly behaved elliptic partial differential equations. (English) Zbl 0434.35008


MSC:

35A20 Analyticity in context of PDEs
35A25 Other special methods applied to PDEs
35J15 Second-order elliptic equations

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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) · Zbl 0231.65034
[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
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