A genuinely stable Lagrange-Galerkin scheme for convection-diffusion problems

作者：Tabata Masahisa^*; Uchiumi Shinya

来源：Japan Journal of Industrial and Applied Mathematics, 2016, 33(1): 121-143.

DOI：10.1007/s13160-015-0196-2

• Lagrange-Galerkin scheme
• Finite element method
• Convectiondiffusion problems
• Exact integration

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 -element we prove error estimates of in -norm and of in -norm. Numerical results reflect these estimates.

• 出版日期2016-2