Abstract
We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.
| Original language | English |
|---|---|
| Pages (from-to) | 121-143 |
| Number of pages | 23 |
| Journal | Japan Journal of Industrial and Applied Mathematics |
| Volume | 33 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2016 Feb 1 |
Keywords
- Convection-diffusion problems
- Exact integration
- Finite element method
- Lagrange–Galerkin scheme
ASJC Scopus subject areas
- Applied Mathematics
- Engineering(all)
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Cite this
Tabata, M., & Uchiumi, S. (2016). A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems. Japan Journal of Industrial and Applied Mathematics, 33(1), 121-143. https://doi.org/10.1007/s13160-015-0196-2