A space–time discontinuous Galerkin finite element method for the Oseen equations on time-dependent flow domains is presented. The algorithm results in a higher order accurate conservative discretization on moving and deforming meshes and is well suited for hp-adaptation. A detailed analysis of the stability of the numerical discretization is given which shows that the algorithm is unconditionally stable, also when equal order polynomial basis functions for the pressure and velocity are used. The accuracy of the space–time discretization is investigated using a detailed hp-error analysis and computations on a model problem.
- Space–time discontinuous Galerkin method
- Oseen equations
- ALE methods
- hp-error analysis
van der Vegt, J. J. W., & Janivita Joto Sudirham, J. J. S. (2008). A space-time discontinuous Galerkin method for the time-dependent Oseen equations. Applied numerical mathematics, 58(WP 08-02/12), 1892-1917. [10.1016/j.apnum.2007.11.010]. https://doi.org/10.1016/j.apnum.2007.11.010