full
search.png

Search

close.png

Cancel

arrow
Volume 33, Issue 1
Graded Meshes for Higher Order FEM

Hans-Görg Roos, L. Teofanov & Zorica Uzelac

DOI: 10.4208/jcm.1405-m4362

J. Comp. Math., 33 (2015), pp. 1-16.

Published online: 2015-02

Preview Full PDF 3602 34346

Cited by

google scholar semantic scholar
Export citation
  • Abstract

A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.

  • Keywords

Singular perturbation, Boundary value problem, Layer-adapted meshes, Graded meshes, Finite element method.

  • AMS Subject Headings

65L11, 65L50, 65L60, 65L70.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Hans-Goerg.Roos@tu-dresden.de (Hans-Görg Roos)

ljiljap@uns.ac.rs (L. Teofanov)

zora@uns.ac.rs (Zorica Uzelac)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-1, author = {Roos , Hans-GörgTeofanov , L. and Uzelac , Zorica}, title = {Graded Meshes for Higher Order FEM}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {1}, pages = {1--16}, abstract = {

A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1405-m4362}, url = {http://global-sci.org/intro/article_detail/jcm/9824.html} }
TY - JOUR T1 - Graded Meshes for Higher Order FEM AU - Roos , Hans-Görg AU - Teofanov , L. AU - Uzelac , Zorica JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 16 PY - 2015 DA - 2015/02 SN - 33 DO - http://doi.org/10.4208/jcm.1405-m4362 UR - https://global-sci.org/intro/article_detail/jcm/9824.html KW - Singular perturbation, Boundary value problem, Layer-adapted meshes, Graded meshes, Finite element method. AB -

A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.

Roos , Hans-GörgTeofanov , L. and Uzelac , Zorica. (2015). Graded Meshes for Higher Order FEM. Journal of Computational Mathematics. 33 (1). 1-16. doi:10.4208/jcm.1405-m4362
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard