Error estimates for linear finite elements on Bakhvalov-type meshes

Hans-Görg Roos

Applications of Mathematics (2006)

  • Volume: 51, Issue: 1, page 63-72
  • ISSN: 0862-7940

Abstract

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For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh.

How to cite

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Roos, Hans-Görg. "Error estimates for linear finite elements on Bakhvalov-type meshes." Applications of Mathematics 51.1 (2006): 63-72. <http://eudml.org/doc/33244>.

@article{Roos2006,
abstract = {For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh.},
author = {Roos, Hans-Görg},
journal = {Applications of Mathematics},
keywords = {numerical analysis; convection-diffusion problem; boundary layer; uniform convergence; convection-diffusion problem; boundary layer; uniform convergence; error estimates; linear finite elements; Shishkin-type meshes; Bakhvalov-type mesh},
language = {eng},
number = {1},
pages = {63-72},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Error estimates for linear finite elements on Bakhvalov-type meshes},
url = {http://eudml.org/doc/33244},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Roos, Hans-Görg
TI - Error estimates for linear finite elements on Bakhvalov-type meshes
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 63
EP - 72
AB - For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh.
LA - eng
KW - numerical analysis; convection-diffusion problem; boundary layer; uniform convergence; convection-diffusion problem; boundary layer; uniform convergence; error estimates; linear finite elements; Shishkin-type meshes; Bakhvalov-type mesh
UR - http://eudml.org/doc/33244
ER -

References

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  2. 10.1016/S0045-7825(02)00630-8, Comput. Methods Appl. Mech. Engrg. 192 (2003), 1061–1105. (2003) Zbl1022.76036MR1960975DOI10.1016/S0045-7825(02)00630-8
  3. Finite Elemente, University textbook of Würzburg, 1998. (1998) 
  4. 10.1016/S0168-9274(01)00051-4, Appl. Numer. Math. 39 (2001), 47–60. (2001) MR1855164DOI10.1016/S0168-9274(01)00051-4
  5. 10.1007/s006070050049, Computing 63 (1999), 27–45. (1999) MR1702159DOI10.1007/s006070050049
  6. Numerical Methods for Singularly Perturbed Differential Equations. Convection-Diffusion and Flow Problems, Springer-Verlag, Berlin, 1996. (1996) MR1477665
  7. Numerical Methods for Problems with Boundary Layers  II, Nauka, Novosibirsk, 2002. (Russian) (2002) MR2029041
  8. 10.1006/jmaa.1997.5581, J.  Math. Anal. Appl. 214 (1997), 36–54. (1997) MR1645503DOI10.1006/jmaa.1997.5581

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