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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

Software:

YSMP
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References:

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[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, ()
[7] Eisenstat, S.C.; Gursky, M.C.; Schultz, M.H.; Sherman, A.H., Yale sparse matrix package I: the symmetric codes, () · Zbl 0492.65012
[8] Hackbusch, W., On the convergence of a multi-grid iteration applied to finite element equations, () · Zbl 0391.65045
[9] Nicolaides, R.A., On the 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, ()
[14] Bank, R.E.; Sherman, A.H., Algorithmic aspects of the multi-level solution of finite element equations, () · 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)
[16] R.E. Bank and A.H. Sherman, “A Comparison of Smoothing Iterations for Multi-level Methods”, these proceedings.
[17] Houstis, E.N.; Rice, J.R., A population of partial differential equations for evaluating methods, () · Zbl 0793.68071
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