New results concerning the DWR method for some nonconforming FEM

Reiner Vanselow

Applications of Mathematics (2012)

  • Volume: 57, Issue: 6, page 551-568
  • ISSN: 0862-7940

Abstract

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This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete -seminorm are derived.

How to cite

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Vanselow, Reiner. "New results concerning the DWR method for some nonconforming FEM." Applications of Mathematics 57.6 (2012): 551-568. <http://eudml.org/doc/246641>.

@article{Vanselow2012,
abstract = {This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete $H^1$-seminorm are derived.},
author = {Vanselow, Reiner},
journal = {Applications of Mathematics},
keywords = {nonconforming finite elements; dual-weighted residual method; a posteriori error estimate; Poisson equation; finite element method; Helmholtz decomposition; Poisson equation; finite element method; a posteriori error estimates; dual-weighted residual method; Helmholtz decomposition},
language = {eng},
number = {6},
pages = {551-568},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New results concerning the DWR method for some nonconforming FEM},
url = {http://eudml.org/doc/246641},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Vanselow, Reiner
TI - New results concerning the DWR method for some nonconforming FEM
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 6
SP - 551
EP - 568
AB - This paper presents a unified framework for the dual-weighted residual (DWR) method for a class of nonconforming FEM. Our approach is based on a modification of the dual problem and uses various ideas from literature which are combined in a new manner. The results are new error identities for some nonconforming FEM. Additionally, a posteriori error estimates with respect to the discrete $H^1$-seminorm are derived.
LA - eng
KW - nonconforming finite elements; dual-weighted residual method; a posteriori error estimate; Poisson equation; finite element method; Helmholtz decomposition; Poisson equation; finite element method; a posteriori error estimates; dual-weighted residual method; Helmholtz decomposition
UR - http://eudml.org/doc/246641
ER -

References

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  1. Ainsworth, M., 10.1137/S0036142903425112, SIAM J. Numer. Anal. 42 (2005), 2320-2341. (2005) Zbl1085.65102MR2139395DOI10.1137/S0036142903425112
  2. Ainsworth, M., A posteriori error estimation for non-conforming quadrilateral finite elements, Int. J. Numer. Anal. Model. 2 (2005), 1-18. (2005) Zbl1071.65141MR2112654
  3. Ainsworth, M., Rankin, R., 10.1137/07070838X, SIAM J. Numer. Anal. 46 (2008), 3207-3232. (2008) Zbl1180.65141MR2448662DOI10.1137/07070838X
  4. Ainsworth, M., Vejchodský, T., 10.1007/s00211-011-0384-1, Numer. Math. 119 (2011), 219-243. (2011) Zbl1229.65194MR2836086DOI10.1007/s00211-011-0384-1
  5. Becker, R., Rannacher, R., 10.1017/S0962492901000010, Acta Numerica 10 (2001), 1-102. (2001) Zbl1105.65349MR2009692DOI10.1017/S0962492901000010
  6. Carstensen, C., Hu, J., Orlando, A., 10.1137/050628854, SIAM J. Numer. Anal. 45 (2007), 68-82. (2007) Zbl1165.65072MR2285845DOI10.1137/050628854
  7. Carstensen, C., Hu, J., 10.1007/s00211-007-0068-z, Numer. Math. 107 (2007), 473-502. (2007) MR2336116DOI10.1007/s00211-007-0068-z
  8. Dari, E., Duran, R., Padra, C., Vampa, V., 10.1051/m2an/1996300403851, RAIRO, Modélisation Math. Anal. Numér. 30 (1996), 385-400. (1996) Zbl0853.65110MR1399496DOI10.1051/m2an/1996300403851
  9. Jr., J. Douglas, Santos, J. E., Sheen, D., Ye, X., 10.1051/m2an:1999161, M2AN, Math. Model. Numer. Anal. 33 (1999), 747-770. (1999) Zbl0941.65115MR1726483DOI10.1051/m2an:1999161
  10. Grajewski, M., Hron, J., Turek, S., 10.1016/j.apnum.2004.09.016, Appl. Numer. Math. 54 (2005), 504-518. (2005) Zbl1074.65123MR2149366DOI10.1016/j.apnum.2004.09.016
  11. Han, H.-D., A finite element approximation of Navier-Stokes equations using nonconforming elements, J. Comput. Math. 2 (1984), 77-88. (1984) Zbl0598.76029
  12. Kanschat, G., Suttmeier, F.-T., 10.1007/s100920050027, Calcolo 36 (1999), 129-141. (1999) Zbl0936.65128MR1742308DOI10.1007/s100920050027
  13. Rannacher, R., Turek, S., 10.1002/num.1690080202, Numer. Methods Partial Differ. Equations 8 (1992), 97-111. (1992) Zbl0742.76051MR1148797DOI10.1002/num.1690080202
  14. Schieweck, F., 10.1051/m2an:2002022, M2AN, Math. Model. Numer. Anal. 36 (2002), 489-503. (2002) Zbl1041.65083MR1918941DOI10.1051/m2an:2002022

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