Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method

Pengzhan Huang

Applications of Mathematics (2014)

  • Volume: 59, Issue: 4, page 361-370
  • ISSN: 0862-7940

Abstract

top
This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.

How to cite

top

Huang, Pengzhan. "Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method." Applications of Mathematics 59.4 (2014): 361-370. <http://eudml.org/doc/261921>.

@article{Huang2014,
abstract = {This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.},
author = {Huang, Pengzhan},
journal = {Applications of Mathematics},
keywords = {Stokes eigenvalue problem; stabilized method; lowest equal-order pair; projection method; superconvergence; Stokes eigenvalue problem; stabilized method; lowest equal-order pair; projection method; superconvergence; finite element; least squares method; numerical tests},
language = {eng},
number = {4},
pages = {361-370},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method},
url = {http://eudml.org/doc/261921},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Huang, Pengzhan
TI - Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 361
EP - 370
AB - This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.
LA - eng
KW - Stokes eigenvalue problem; stabilized method; lowest equal-order pair; projection method; superconvergence; Stokes eigenvalue problem; stabilized method; lowest equal-order pair; projection method; superconvergence; finite element; least squares method; numerical tests
UR - http://eudml.org/doc/261921
ER -

References

top
  1. Bochev, P., Dohrmann, C. R., Gunzburger, M. D., 10.1137/S0036142905444482, SIAM J. Numer. Anal. 44 (2006), 82-101 (electronic). (2006) Zbl1145.76015MR2217373DOI10.1137/S0036142905444482
  2. Chen, H., Jia, S., Xie, H., 10.1007/s10492-009-0015-7, Appl. Math., Praha 54 (2009), 237-250. (2009) Zbl1212.65431MR2530541DOI10.1007/s10492-009-0015-7
  3. Chen, W., Lin, Q., 10.1007/s10492-006-0006-x, Appl. Math., Praha 51 (2006), 73-88. (2006) Zbl1164.65489MR2197324DOI10.1007/s10492-006-0006-x
  4. Chen, H., Wang, J., 10.1137/S0036142902410039, SIAM J. Numer. Anal. 41 (2003), 1318-1338 (electronic). (2003) Zbl1058.65118MR2034883DOI10.1137/S0036142902410039
  5. Chou, S. H., Ye, X., 10.1016/j.cma.2006.10.025, Comput. Methods Appl. Mech. Eng. 196 (2007), 3706-3712. (2007) Zbl1173.65354MR2339996DOI10.1016/j.cma.2006.10.025
  6. Cui, M., Ye, X., 10.1002/num.20399, Numer. Methods Partial Differ. Equations 25 (2009), 1212-1230. (2009) Zbl1170.76037MR2541808DOI10.1002/num.20399
  7. Hecht, F., Pironneau, O., Hyaric, A. Le, Ohtsuka, K., FREEFEM++, version 2.3-3, 2008. Software avaible at http://www.freefem.org, . 
  8. Heimsund, B. O., Tai, X. C., Wang, J. P., 10.1137/S003614290037410X, SIAM J. Numer. Anal. 40 (2002), 1263-1280. (2002) Zbl1047.65095MR1951894DOI10.1137/S003614290037410X
  9. Huang, P. Z., He, Y. N., Feng, X. L., Numerical investigations on several stabilized finite element methods for the Stokes eigenvalue problem, Math. Probl. Eng. 2011 (2011), Article ID 745908, pp. 14. (2011) Zbl1235.74286MR2826898
  10. Huang, P. Z., He, Y. N., Feng, X. L., 10.1007/s10483-012-1575-7, Appl. Math. Mech., Engl. Ed. 33 (2012), 621-630. (2012) Zbl1266.65192MR2978223DOI10.1007/s10483-012-1575-7
  11. Huang, P. Z., Zhang, T., Ma, X. L., 10.1016/j.camwa.2011.10.012, Comput. Math. Appl. 62 (2011), 4249-4257. (2011) Zbl1236.76017MR2859980DOI10.1016/j.camwa.2011.10.012
  12. Jia, S., Xie, H., Yin, X., Gao, S., 10.1007/s10492-009-0001-0, Appl. Math., Praha 54 (2009), 1-15. (2009) Zbl1212.65434MR2476018DOI10.1007/s10492-009-0001-0
  13. Li, J., 10.1002/mma.1051, Math. Methods Appl. Sci. 32 (2009), 470-479. (2009) MR2493591DOI10.1002/mma.1051
  14. Li, J., He, Y. N., 10.1002/num.20188, Numer. Methods Partial Differ. Equations 23 (2007), 421-436. (2007) Zbl1107.76046MR2289460DOI10.1002/num.20188
  15. Li, J., He, Y. N., 10.1016/j.cam.2007.02.015, J. Comput. Appl. Math. 214 (2008), 58-65. (2008) Zbl1132.35436MR2391672DOI10.1016/j.cam.2007.02.015
  16. Li, J., He, Y. N., Wu, J. H., 10.1016/j.na.2011.06.033, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74 (2011), 6499-6511. (2011) Zbl1227.65115MR2834057DOI10.1016/j.na.2011.06.033
  17. Li, J., Mei, L. Q., Chen, Z. X., 10.1002/num.20610, Numer. Methods Partial Differ. Equations 28 (2012), 115-126. (2012) Zbl1234.65038MR2864661DOI10.1002/num.20610
  18. Li, J., Wang, J., Ye, X., Superconvergence by L 2 -projections for stabilized finite element methods for the Stokes equations, Int. J. Numer. Anal. Model. 6 (2009), 711-723. (2009) MR2574761
  19. Liu, H. P., Yan, N. N., 10.1016/j.cma.2012.04.009, Comput. Methods Appl. Mech. Eng. 233/236 (2012), 81-91. (2012) Zbl1253.74107MR2924022DOI10.1016/j.cma.2012.04.009
  20. Lovadina, C., Lyly, M., Stenberg, R., 10.1002/num.20342, Numer. Methods Partial Differ. Equations 25 (2009), 244-257. (2009) Zbl1169.65109MR2473688DOI10.1002/num.20342
  21. Wang, J., Superconvergence analysis for finite element solutions by the least-squares surface fitting on irregular meshes for smooth problems, J. Math. Study 33 (2000), 229-243. (2000) Zbl0987.65108MR1868268
  22. Wang, J., Ye, X., 10.1137/S003614290037589X, SIAM J. Numer. Anal. 39 (2001), 1001-1013 (electronic). (2001) Zbl1002.65118MR1860454DOI10.1137/S003614290037589X
  23. Ye, X., 10.1002/num.1036, Numer. Methods Partial Differ. Equations 18 (2002), 143-154. (2002) Zbl1003.65121MR1902289DOI10.1002/num.1036
  24. Yin, X., Xie, H., Jia, S., Gao, S., 10.1016/j.cam.2007.03.028, J. Comput. Appl. Math. 215 (2008), 127-141. (2008) Zbl1149.65090MR2400623DOI10.1016/j.cam.2007.03.028

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.