Questions tagged [divergence-free]

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Discrete divergence free functions

I'm studying the weak formulation of NS equations. During the analysis, the book I'm using (Quarteroni-Valli, page 301-302), defined $$Z_h=\{v_h \in V_h: (\operatorname{div}(v_h),q_h)=0 \quad \forall ...
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Intuitively, what does it mean for a solution to be divergence free?

I have always been interested in generating discrete approximations that tend to mimic the properties of their continuum counterparts. Usually, one approximation that is desired is that the discrete ...
4
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Compute 2d velocity field with given curl and zero divergence

Given $\omega$ I want to compute the vector $q=(u,v)$ such that $$ v_x - u_y = \omega, \qquad u_x + v_y = 0, \qquad \textrm{in } \Omega $$ and $$ u n_x + v n_y = 0, \qquad \textrm{on } \partial\Omega $...