Exponential convergence of mixed hp-DGFEM for the incompressible Navier–Stokes equations in ℝ2
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Bibliographic record
Abstract
Abstract In a polygon $\varOmega \subset \mathbb{R}^2$ we consider mixed $hp$-discontinuous Galerkin approximations of the stationary, incompressible Navier–Stokes equations, subject to no-slip boundary conditions. We use geometrically corner-refined meshes and $hp$ spaces with linearly increasing polynomial degrees. Based on recent results on analytic regularity of velocity field and pressure of Leray solutions in $\varOmega$, we prove exponential rates of convergence of the mixed $hp$-discontinuous Galerkin finite element method, with respect to the number of degrees of freedom, for small data which is piecewise analytic.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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