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Volume 7, Issue 3
Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes

L. Kaland & H.-G. Roos

Int. J. Numer. Anal. Mod., 7 (2010), pp. 593-606.

Published online: 2010-07

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  • Abstract

A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the $\theta$-scheme as for discontinuous Galerkin in time.

  • Keywords

Convection-diffusion, transient, finite element, Shishkin mesh, time discretization.

  • AMS Subject Headings

65N12, 65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-593, author = {L. Kaland and H.-G. Roos}, title = {Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {593--606}, abstract = {

A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the $\theta$-scheme as for discontinuous Galerkin in time.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/740.html} }
TY - JOUR T1 - Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes AU - L. Kaland & H.-G. Roos JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 593 EP - 606 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/740.html KW - Convection-diffusion, transient, finite element, Shishkin mesh, time discretization. AB -

A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the $\theta$-scheme as for discontinuous Galerkin in time.

L. Kaland and H.-G. Roos. (2010). Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes. International Journal of Numerical Analysis and Modeling. 7 (3). 593-606. doi:
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