All Questions
Tagged with fa.functional-analysis finite-element-method
7 questions
6
votes
1
answer
2k
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Finite element method inverse estimate
$\DeclareMathOperator\diam{diam}$Looking for a proof in the literature of the following lemma:
Let $K\subset\mathbb{R}^d$ be a bounded domain. Let $P_X$ be a finite dimensional subspace of $\mathcal{...
- 3,217
2
votes
0
answers
66
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Continuity of weak solution of elliptic PDE
I am investigating the following standard elliptic PDE with mixed Dirichlet-Neumann boundary condition:
$-\Delta u=f$ on $\Omega$; $u=0$ on $\Gamma_D$; $\left<n,\nabla u=g\right>$ on $\Gamma_N$
...
- 21
1
vote
1
answer
441
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Generalized Lax-Milgram for Weak Formulation of 1D Linear Schrodinger
I am interested in the variational formulation of the 1D Schrodinger equation:
$i u_t- \beta u_{xx} = 0 $ and $u(x,0)=u_0(x)$ which upon integration by parts yields:
$i(u_t,v) + \beta (u_x,v_x) = 0$ ...
1
vote
1
answer
207
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How to solve Poissons equation using FEM with integral BC?
I have a 3-dimensional domain D, with 3 types of BC which I am trying to solve the Poisson equation on. $$-\nabla \cdot (\sigma(x,y,z)\nabla u)=0$$
Insulator (Neumann BC)
Electrode set at some ...
- 11
1
vote
0
answers
47
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Holomorphic "quasi-interpolation" of a function sequence
I am interested in some sort of analytic interpolation. A toy version of my problem is as follows. Let $V \subset \mathbb{C}$ be a complex neighborhood of $[0,1]$. Assume there is some bounded ...
- 981
1
vote
0
answers
80
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Unclear inequality of L2 norms (Poisson equation for modeling flow)
I encountered a problem working through a paper about modeling flow with the use of the Poisson equation (source given below). There appears an inequality of L2 norms I don't understand so far. Your ...
- 11
1
vote
0
answers
80
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Estimate a projection from a product space of $H^1(\mathbb{R}^3)$ to a finite dimensional space
Let $\mathcal{H}=(H^1(\mathbb{R}^3))^N$ be the product space with the associated norm
$$
\Vert U\Vert_1=\left(\sum^N_{i=1}\Vert u_i\Vert_1^2\right)^{1/2}
$$
where $U=(u_1,u_2,...,u_N)\in\mathcal{H}$. ...
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