Questions tagged [mixed-formulation]

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Locking phenomena for $P1 - P0$ elements

Consider the Stokes problem and the usual divergence operator $B:V \rightarrow Q'$, $\langle Bv, q\rangle = b(v,q)=(\operatorname{div} v,q)$ and its discrete versione $B_h : V_h \rightarrow Q_h'$. In ...
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About the condition $\ker(B_h) \subset \ker(B)$ in mixed finite elements formulation

I'm studying mixed finite elements. The problem is a classical saddle-point one: we seek for $(u,p)$ in $V \times Q$: $$A u + B^t p = f$$ $$Bu = g$$ where $A: V \rightarrow V', B:V \rightarrow Q'$ ...
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Biharmonic equation mixed formulation, mixed boundary conditions

I have the following formulation of the biharmonic equation: $$\Delta u(x) = v(x), \quad x \in \Omega\setminus K$$ $$-\Delta v = 0, \quad x \in \Omega\setminus K$$ $$u(x) = g(x), \quad x \in K$$ $$v(x)...