Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D

Hans-Görg Roos; Martin Schopf

Applications of Mathematics (2012)

  • Volume: 57, Issue: 2, page 97-108
  • ISSN: 0862-7940

Abstract

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So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.

How to cite

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Roos, Hans-Görg, and Schopf, Martin. "Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D." Applications of Mathematics 57.2 (2012): 97-108. <http://eudml.org/doc/247053>.

@article{Roos2012,
abstract = {So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.},
author = {Roos, Hans-Görg, Schopf, Martin},
journal = {Applications of Mathematics},
keywords = {finite element method; singular perturbation; convection-diffusion problem; Bakhvalov-type meshes; layer-adapted meshes; optimal error estimates; exponential boundary layers; finite element method; singular perturbation; convection-diffusion problem; Bakhvalov-type mesh; layer-adapted mesh; optimal error estimates; exponential boundary layers},
language = {eng},
number = {2},
pages = {97-108},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D},
url = {http://eudml.org/doc/247053},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Roos, Hans-Görg
AU - Schopf, Martin
TI - Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 2
SP - 97
EP - 108
AB - So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
LA - eng
KW - finite element method; singular perturbation; convection-diffusion problem; Bakhvalov-type meshes; layer-adapted meshes; optimal error estimates; exponential boundary layers; finite element method; singular perturbation; convection-diffusion problem; Bakhvalov-type mesh; layer-adapted mesh; optimal error estimates; exponential boundary layers
UR - http://eudml.org/doc/247053
ER -

References

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  5. Lin{ß}, T., Stynes, M., 10.1006/jmaa.2001.7550, J. Math. Anal. Appl. 261 (2001), 604-632. (2001) Zbl1200.35046MR1853059DOI10.1006/jmaa.2001.7550
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  7. O'Riordan, E., Shiskin, G., 10.1016/j.cam.2006.06.002, J. Comput. Appl. Math. 206 (2007), 136-145. (2007) MR2333841DOI10.1016/j.cam.2006.06.002
  8. Roos, H.-G., Lin{ß}, T., 10.1007/s006070050049, Computing 63 (1999), 27-45. (1999) Zbl0931.65085MR1702159DOI10.1007/s006070050049
  9. Roos, H.-G., 10.1007/s10492-006-0005-y, Appl. Math. 51 (2006), 63-72. (2006) Zbl1164.65486MR2197323DOI10.1007/s10492-006-0005-y
  10. Roos, H.-G., Stynes, M., Tobiska, L., Robust Numerical Methods for Singularly Perturbed Differential Equations, Springer Berlin (2008). (2008) Zbl1155.65087MR2454024
  11. Stynes, M., O'Riordan, E., 10.1006/jmaa.1997.5581, J. Math. Anal. Appl. 214 (1997), 36-54. (1997) Zbl0917.65088MR1645503DOI10.1006/jmaa.1997.5581
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