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The skew convective form for incompressible flow
Definition
Let be a bounded connected Lipschitz domain with , and let as in Stokes velocity and pressure spaces and weak forms. For , define the real skew convective form The middle and last slots are displayed separately to emphasize . In particular . The integrals are well-defined on by Continuity, energy cancellation, and Sobolev bounds for skew convection ↗. If additionally , then .
Depends on
Used by
- An energy Navier–Stokes velocity on the square without endpoint-integrable pressure Counterexample
- Graded MINI mass initialization can destroy the smooth instantaneous pressure rate Counterexample
- Energy weak solutions of incompressible Navier–Stokes Definition
- Solenoidal energy weak velocity for incompressible Navier–Stokes Definition
- The mixed mini-element backward Euler Navier–Stokes scheme Definition
- Continuity, energy cancellation, and Sobolev bounds for skew convection Lemma
- Integrated pressure recovery and MINI pressure-primitive convergence Lemma
- Uniqueness and strong trace for two-dimensional solenoidal energy velocities Lemma
- Well-definedness of the finite-dimensional mini backward Euler equations Lemma
- Backward Euler MINI step existence and discrete energy bound Theorem
- First-order smooth pressure-primitive error for backward Euler MINI Theorem
- Smooth-branch velocity error for backward Euler MINI Theorem
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Endre Süli and Tabea Tscherpel, Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids, arXiv:1804.02264v1 (standard reference, not scraped)
- Xiaoming He, Introduction and Basic Implementation for Finite Element Methods, Chapter 9: Finite elements for 2D unsteady Navier–Stokes equations (standard reference, not scraped)