
Spacetime Euler discretization schemes for the stochastic 2D NavierStokes equations
We prove that the implicit time Euler scheme coupled with finite element...
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Numerical analysis of 2D Navier–Stokes equations with additive stochastic forcing
We propose and study a temporal, and spatiotemporal discretisation of t...
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Numerical convergence of discrete extensions in a spacetime finite element, fictitious domain method for the NavierStokes equations
A key ingredient of our fictitious domain, higher order spacetime cut f...
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Convergence and error estimates for a finite difference scheme for the multidimensional compressible NavierStokes system
We prove convergence of a finite difference approximation of the compres...
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A framework for approximation of the Stokes equations in an axisymmetric domain
We develop a framework for solving the stationary, incompressible Stokes...
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Continuous Data Assimilation for the Three Dimensional NavierStokes Equations
In this paper, we provide conditions, based solely on the observed data,...
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Minimizing Quadratic Functions in Constant Time
A samplingbased optimization method for quadratic functions is proposed...
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A fully spacetime leastsquares method for the unsteady NavierStokes system
We introduce and analyze a spacetime leastsquares method associated to the unsteady NavierStokes system. Weak solution in the two dimensional case and regular solution in the three dimensional case are considered. From any initial guess, we construct a minimizing sequence for the leastsquares functional which converges strongly to a solution of the NavierStokes system. After a finite number of iterates related to the value of the viscosity constant, the convergence is quadratic. Numerical experiments within the two dimensional case support our analysis. This globally convergent leastsquares approach is related to the damped Newton method when used to solve the NavierStokes system through a variational formulation.
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