Stable Crank--Nicolson discretisation for incompressible miscible displacement problems of low regularity
- Jensen, Max
- Müller, Rüdiger
2010 Mathematics Subject Classification
- 65M60 65M12 76S05
- discontinuous Galerkin, low regularity, Crank-Nicolson
In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart of the analysis is the proof of convergence under low regularity requirements. Numerical experiments demonstrate that the proposed method exhibits second-order convergence for smooth and robustness for rough problems.
- Numerical Mathematics and Advanced Applications 2009, Part 2, G. Kreiss, P. Lötstedt, A. Målqvist, M. Neytcheva, eds., Springer, Heidelberg et al., pp. 469--477