Grid adjustment based on a posteriori error estimators

Karel Segeth

Applications of Mathematics (1993)

  • Volume: 38, Issue: 6, page 488-504
  • ISSN: 0862-7940

Abstract

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The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.

How to cite

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Segeth, Karel. "Grid adjustment based on a posteriori error estimators." Applications of Mathematics 38.6 (1993): 488-504. <http://eudml.org/doc/15769>.

@article{Segeth1993,
abstract = {The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.},
author = {Segeth, Karel},
journal = {Applications of Mathematics},
keywords = {grid adjustment; principle of equidistribution of monitor; a posteriori error estimate; parabolic equation; finite element method; method of lines; grid adjustment; finite element method of lines; error estimators; parabolic systems},
language = {eng},
number = {6},
pages = {488-504},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Grid adjustment based on a posteriori error estimators},
url = {http://eudml.org/doc/15769},
volume = {38},
year = {1993},
}

TY - JOUR
AU - Segeth, Karel
TI - Grid adjustment based on a posteriori error estimators
JO - Applications of Mathematics
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 38
IS - 6
SP - 488
EP - 504
AB - The adjustment of one-dimensional space grid for a parabolic partial differential equation solved by the finite element method of lines is considered in the paper. In particular, the approach based on a posteriori error indicators and error estimators is studied. A statement on the rate of convergence of the approximation of error by estimator to the error in the case of a system of parabolic equations is presented.
LA - eng
KW - grid adjustment; principle of equidistribution of monitor; a posteriori error estimate; parabolic equation; finite element method; method of lines; grid adjustment; finite element method of lines; error estimators; parabolic systems
UR - http://eudml.org/doc/15769
ER -

References

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  2. S. Adjerid J.E. Flaherty Y.J. Wang, A Posteriori Error Estimation with Finite Element Methods of Lines for One-Dimensional Parabolic Systems, Tech. Report 91-1, Troy, NY, Dept. of Computer Science, Rensselaer Polytechnic Institute, 1991. (1991) MR1217436
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  9. J. Hugger, Density Representation of Finite Element Meshes for One and Two Dimensional Problems, Non-Singular or with Point Singularities, Part 1 and 2, Preprint, College Park, MD, IPST, University of Maryland, 1992. (1992) MR1195582
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  12. J. T. Oden G. F. Carey, Finite Elements: Mathematical Aspects, Vol. IV, Englewood Cliffs, NJ, Prentice-Hall, 1983. (1983) MR0767806
  13. L. R. Petzold, A Description of DDASSL: A Differential/Algebraic System Solver, Sandia Report No. Sand 82-8637, Livermore, CA, Sandia National Laboratory, 1982. (1982) MR0751605
  14. Y. Ren R. D. Russell, Moving Mesh Techniques Based upon Equidistribution, and Their Stability, Preprint, Burnaby, B.C., Dept. of Mathematics and Statistics, Simon Fraser University, 1989. (1989) MR1185646
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