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Displaying 281 –
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We study a two-grid scheme fully discrete in time and
space for solving the Navier-Stokes system. In the first step, the
fully non-linear problem is discretized in space on a coarse grid
with mesh-size H and time step k. In the second step, the
problem is discretized in space on a fine grid with mesh-size h
and the same time step, and linearized around the velocity uH
computed in the first step. The two-grid strategy is motivated by
the fact that under suitable assumptions, the contribution of
uH...
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as...
We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the...
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