A stable and optimal complexity solution method for mixed finite element discretizations

Jan Brandts; Rob Stevenson

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 153-161
  • ISSN: 0862-7959

Abstract

top
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inhomogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally gives the Lagrangian multiplier. We concentrate on aspects involved in the first and third step mainly, and advertise a multi-level method that allows for a stable computation of the intermediate and final quantities in optimal computational complexity.

How to cite

top

Brandts, Jan, and Stevenson, Rob. "A stable and optimal complexity solution method for mixed finite element discretizations." Mathematica Bohemica 127.2 (2002): 153-161. <http://eudml.org/doc/249054>.

@article{Brandts2002,
abstract = {We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inhomogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally gives the Lagrangian multiplier. We concentrate on aspects involved in the first and third step mainly, and advertise a multi-level method that allows for a stable computation of the intermediate and final quantities in optimal computational complexity.},
author = {Brandts, Jan, Stevenson, Rob},
journal = {Mathematica Bohemica},
keywords = {mixed finite elements; multi-level solver; mixed finite elements; multi-level solver},
language = {eng},
number = {2},
pages = {153-161},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A stable and optimal complexity solution method for mixed finite element discretizations},
url = {http://eudml.org/doc/249054},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Brandts, Jan
AU - Stevenson, Rob
TI - A stable and optimal complexity solution method for mixed finite element discretizations
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 153
EP - 161
AB - We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inhomogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally gives the Lagrangian multiplier. We concentrate on aspects involved in the first and third step mainly, and advertise a multi-level method that allows for a stable computation of the intermediate and final quantities in optimal computational complexity.
LA - eng
KW - mixed finite elements; multi-level solver; mixed finite elements; multi-level solver
UR - http://eudml.org/doc/249054
ER -

References

top
  1. 10.1007/BF01436561, Numer. Math. 20 (1973), 179–192. (1973) MR0359352DOI10.1007/BF01436561
  2. 10.1137/0729042, SIAM J. Numer. Anal. 29 (1992), 647–678. (1992) Zbl0759.65080MR1163350DOI10.1137/0729042
  3. 10.1023/A:1014217225870, Advances Comput. Math. 15 (2001), 61–77. (2001) Zbl0996.65120MR1887729DOI10.1023/A:1014217225870
  4. 10.1137/0914065, SIAM J. Sci. Comput. 14 (1993), 1072–1088. (1993) MR1232176DOI10.1137/0914065
  5. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, RAIRO Anal. Numér. 8 (1974), 129–151. (1974) Zbl0338.90047MR0365287
  6. 10.1051/m2an/1994280403771, RAIRO Modèl. Math. Anal. Numér. 28 (1994), 377–398. (1994) MR1288504DOI10.1051/m2an/1994280403771
  7. Finite Element Methods for Navier-Stokes Equations. Theory and Algorithms, Springer Series in Computational Mathematics, Springer, Berlin, 1986. (1986) MR0851383
  8. 10.1007/s002110050419, Numer. Math. 82 (1999), 253–279. (1999) MR1685461DOI10.1007/s002110050419
  9. 10.1007/BF02238356, Computing 57 (1996), 25–48. (1996) MR1398269DOI10.1007/BF02238356
  10. A mixed finite element method for 2nd order elliptic problems, Math. Aspects Finite Elem. Math., Proc. Conf. Rome 1975. Lect. Notes Math. 606 (1977), 292–315. (1977) MR0483555
  11. A stable, direct solver for the gradient equation, Math. Comp (to appear). (to appear) Zbl1012.65126MR1933813
  12. 10.1007/s002110050138, Numer. Math. 71 (1995), 121–134. (1995) MR1339734DOI10.1007/s002110050138

NotesEmbed ?

top

You must be logged in to post comments.