Abstract
Subroutine PLTMG is a Fortran program for solving self-adjoint elliptic boundary value problems in general regions ofR 2. It is based on a piecewise linear triangle finite element method, an adaptive grid refinement procedure, and a multi-level iterative method to solve the resulting sets of linear equations. In this work we describe the method and present some numerical results and comparisons.
Zusammenfassung
Das Unterprogramm PLTMG ist ein FORTRAN-Programm zur Lösung selbstadjungierter elliptischer Randwertprobleme für beliebige Bereiche desR 2. Es basiert auf einer stückweise-linearen Finite-Element-Methode, einer adaptiven Gitterverfeinerungsmethode und einer mehrstufigen iterativen Methode zur Lösung des resultierenden Systems linearer Gleichungen. In dieser Arbeit wird die Methode beschrieben, und einige numerische Ergebnisse und Vergleiche werden dargelegt.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Babuška, I., Rheinboldt, W. C.: Error estimates for adaptive finite element computations. SIAM J. Numer. Anal.15, 736–754 (1978).
Babuška, I., Rheinboldt, W. C.: Analysis of optimal finite-element meshes inR 1. Math. of Comp.33, 435–464 (1979).
Bakhvalov, N. S.: On the convergence of a relaxation method with natural constraints on the elliptic operator. Zh. Vÿchisl. Mat. mat.6, 861–885 (1966).
Bank, R. E., Dupont, T.: An optimal order process for solving finite element equations. (Revised January 1978), submitted.
Brandt, A.: Multi-level adaptive solutions to boundary value problems. Math. of Comp.31, 333–390 (1977).
Grimes, R. G., Kincaid, D. R., MacGregor, W. I., Young, D. M.: Adaptive iterative algorithms using symmetric sparse storage. Report CNA 139, Center for Numerical Analysis, University of Texas at Austin, August, 1978.
Eisenstat, S. C., Gursky, M. C., Schultz, M. H., Sherman, A. H.: Yale sparse matrix package I: The symmetric codes. Research Report No. 112, Dept. of Computer Science, Yale University, 1977.
Hackbusch, W.: On the convergence of multi-grid iterations. Beiträge Numer. Math.9 (to appear).
Nicolaides, R. A.: On thel 2 convergence of an algorithm for solving finite element equations. Math. of Comp.31, 892–906 (1977).
Oden, J. T., Reddy, J. N.: An introduction to the mathematical theory of finite elements. J. Wiley 1976.
Strang, G., Fix, G.: An analysis of the finite element method. Prentice-Hall 1973.
Varga, R. S.: Matrix iterative analysis. Prentice-Hall 1962.
Young, D.: Iterative solution of large linear systems. Academic Press 1971.
Bank, R. E., Sherman, A. H.: Algorithmic aspects of the multi-level solution of finite element equations. Report CNA 144, Center for Numerical Analysis, University of Texas at Austin, October 1978.
Astrakhantsev, G. P.: An iterative method of solving elliptic net problems. Zh. Vÿchisl. Mat. mat.11, 439–448 (1971).
Chandra, R.: Conjugate gradient methods for partial differential equations. Ph. D. Dissertation, Yale University, 1978.
Author information
Authors and Affiliations
Additional information
A version of this paper was presented as paper SPE 7683 at the 1979 Society of Petroleum Engineers of AIME Symposium on Reservoir Simulation held in Denver, Colorado, February 1–2, 1979. Work supported in part by the National Aeronautics and Space Administration under grant NSG-1632.
The work of this author was supported in part by the U.S. Air Force Office of Scientific Research under contract F49620-77-C-0037.
Rights and permissions
About this article
Cite this article
Bank, R.E., Sherman, A.H. An adaptive, multi-level method for elliptic boundary value problems. Computing 26, 91–105 (1981). https://doi.org/10.1007/BF02241777
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02241777