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


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


Full Text: DOI


[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}, () · 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, ()
[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
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.