Abstract
In this article, we obtain an optimal best-approximation-type result for fully discrete approximations of the transient Stokes problem. For the time discretization, we use the discontinuous Galerkin method and for the spatial discretization we use standard finite elements for the Stokes problem satisfying the discrete inf-sup condition. The analysis uses the technique of discrete maximal parabolic regularity. The results require only natural assumptions on the data and do not assume any additional smoothness of the solutions.
Original language | English |
---|---|
Pages (from-to) | 852-880 |
Number of pages | 29 |
Journal | IMA Journal of Numerical Analysis |
Volume | 43 |
Issue number | 2 |
DOIs | |
State | Published - 1 Mar 2023 |
Keywords
- a priori estimates
- best approximation
- discontinuous Galerkin method
- finite elements
- pointwise error estimates
- transient Stokes