Spectral methods for singular perturbation problems

Wilhelm Heinrichs

Applications of Mathematics (1994)

  • Volume: 39, Issue: 3, page 161-188
  • ISSN: 0862-7940

Abstract

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We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented.

How to cite

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Heinrichs, Wilhelm. "Spectral methods for singular perturbation problems." Applications of Mathematics 39.3 (1994): 161-188. <http://eudml.org/doc/32877>.

@article{Heinrichs1994,
abstract = {We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented.},
author = {Heinrichs, Wilhelm},
journal = {Applications of Mathematics},
keywords = {spectral methods; singular perturbation; stabilization; domain decomposition; iterative solver; multigrid method; Mehrstellen-method; numerical examples; singular perturbation; advection- diffusion equations; spectral method; artificial viscosity; boundary layer; domain decomposition; relaxation; convergence; multigrid method},
language = {eng},
number = {3},
pages = {161-188},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectral methods for singular perturbation problems},
url = {http://eudml.org/doc/32877},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Heinrichs, Wilhelm
TI - Spectral methods for singular perturbation problems
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 3
SP - 161
EP - 188
AB - We study spectral discretizations for singular perturbation problems. A special technique of stabilization for the spectral method is proposed. Boundary layer problems are accurately solved by a domain decomposition method. An effective iterative method for the solution of spectral systems is proposed. Suitable components for a multigrid method are presented.
LA - eng
KW - spectral methods; singular perturbation; stabilization; domain decomposition; iterative solver; multigrid method; Mehrstellen-method; numerical examples; singular perturbation; advection- diffusion equations; spectral method; artificial viscosity; boundary layer; domain decomposition; relaxation; convergence; multigrid method
UR - http://eudml.org/doc/32877
ER -

References

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  11. 10.1016/0021-9991(80)90005-4, J. Comp. Phys. 37 (1980), 70–92. (1980) MR0584322DOI10.1016/0021-9991(80)90005-4
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  13. 10.1016/0021-9991(82)90063-8, J. Comp. Phys. 48 (1982), 485–501. (1982) MR0755459DOI10.1016/0021-9991(82)90063-8
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