An optimal-order multigrid method for 𝑃1 nonconforming finite elements

An optimal-order multigrid method for $\textrm {P}1$ nonconforming finite elements
HTML articles powered by AMS MathViewer

by Susanne C. Brenner PDF

Math. Comp. 52 (1989), 1-15 Request permission

An optimal-order multigrid method for solving second-order elliptic boundary value problems using P1 nonconforming finite elements is developed.

References

Randolph E. Bank and Todd Dupont, An optimal order process for solving finite element equations, Math. Comp. 36 (1981), no. 153, 35–51. MR 595040, DOI 10.1090/S0025-5718-1981-0595040-2
D. Braess and W. Hackbusch, A new convergence proof for the multigrid method including the $V$-cycle, SIAM J. Numer. Anal. 20 (1983), no. 5, 967–975. MR 714691, DOI 10.1137/0720066
Philippe G. Ciarlet, The finite element method for elliptic problems, Studies in Mathematics and its Applications, Vol. 4, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1978. MR 0520174
M. Crouzeix and P.-A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge 7 (1973), no. R-3, 33–75. MR 343661
M. Fortin and M. Soulie, A nonconforming piecewise quadratic finite element on triangles, Internat. J. Numer. Methods Engrg. 19 (1983), no. 4, 505–520. MR 702056, DOI 10.1002/nme.1620190405
Pierre Grisvard, Behavior of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain, Numerical solution of partial differential equations, III (Proc. Third Sympos. (SYNSPADE), Univ. Maryland, College Park, Md., 1975) Academic Press, New York, 1976, pp. 207–274. MR 0466912

Multi-Grid Methods and Applications

Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973. MR 0443377
Klaus Stüben and Ulrich Trottenberg, Multigrid methods: fundamental algorithms, model problem analysis and applications, Multigrid methods (Cologne, 1981) Lecture Notes in Math., vol. 960, Springer, Berlin-New York, 1982, pp. 1–176. MR 685773
François Thomasset, Implementation of finite element methods for Navier-Stokes equations, Springer Series in Computational Physics, Springer-Verlag, New York-Berlin, 1981. MR 720192, DOI 10.1007/978-3-642-87047-7