Discontinuous Galerkin finite element heterogeneous multiscale method for advection-diffusion problems with multiple scales
| Autor: | Martin Huber, Assyr Abdulle |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Homogenization
Advection Applied Mathematics Numerical analysis Mathematical analysis Discontinuous Galerkin methods Heterogeneous multiscale method Homogenization (chemistry) Finite element method Computational Mathematics Discontinuous Galerkin method Discontinuous galerkin discretization A priori and a posteriori Macro Inf-sup condition Variational crime Advection-diffusion Mathematics |
| Zdroj: | Numerische Mathematik |
| Popis: | A discontinuous Galerkin finite element heterogeneous multiscale method is proposed for advection---diffusion problems with highly oscillatory coefficients. The method is based on a coupling of a discontinuous Galerkin discretization for an effective advection---diffusion problem on a macroscopic mesh, whose a priori unknown data are recovered from micro finite element calculations on sampling domains within each macro element. The computational work involved is independent of the high oscillations in the problem at the smallest scale. The stability of our method (depending on both macro and micro mesh sizes) is established for both diffusion dominated and advection dominated regimes without any assumptions about the type of heterogeneities in the data. Fully discrete a priori error bounds are derived for locally periodic data. Numerical experiments confirm the theoretical error estimates. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|