Questions tagged [mixed-formulation]

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4
votes
2answers
131 views

Is their a book/paper about mixed finite element method for engineering students (non-math)?

There are a lot of books about FEM, which are really friendly to engineering students. Through these books, we can know how to use shape/test functions based on the variational principle. But I'd like ...
1
vote
1answer
108 views

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 ...
5
votes
0answers
145 views

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 $A: V \rightarrow V', B:V \rightarrow Q'$ ...
1
vote
3answers
142 views

Stable finite elements for the mixed form of the elasticity equations

The mixed form of the elasticity equations is to find the unique critical point of the Hellinger-Reissner functional $$J(u, \sigma) = \int_\Omega\left(\frac{1}{2}A\sigma : \sigma - (\nabla\cdot\sigma)\...
1
vote
0answers
128 views

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)...