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Jung, Chang-Yeol
Analysis and computational methods Lab
Research Interests
  • Analysis, singular perturbations, uncertainty, numerical methods

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Construction of boundary layer elements for singularly perturbed convection-diffusion equations and L(2)-stability analysis

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Title
Construction of boundary layer elements for singularly perturbed convection-diffusion equations and L(2)-stability analysis
Author
Jung, Chang-YeolTemam, R.
Keywords
Boundary layer; Boundary layer element; Convection-diffusion; Enriched subspaces; Exponentially fitted splines; Finite elements; Singularly perturbed problem; Stability
Issue Date
2008-12
Publisher
ISCI-INST SCIENTIFIC COMPUTING & INFORMATION
Citation
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, v.5, no.4, pp.729 - 748
Abstract
It has been demonstrated that the ordinary boundary layer elements play an essential role in the finite element approximations for singularly perturbed problems producing ordinary boundary layers. Here we revise the element so that it has a small compact support and hence the resulting linear system becomes sparse, more precisely, block tridiagonal. We prove the validity of the revised element for some singularly perturbed convection-diffusion equations via numerical simulations and via the H1-approximation error analysis. Furthermore due to the compact structure of the boundary layer we are able to prove the L2-stability analysis of the scheme and derive the L2-error approximations.
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ISSN
1705-5105
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