Lines Matching refs:u

14 …lem, posed as a weak form on a Hilbert space $V^p \subset H^1$, i.e., find $u \in V^p$ such that f…
17 \langle v,u \rangle = \langle v,f \rangle ,
20 …v,u\rangle$ and $\langle v,f\rangle$ express the continuous bilinear and linear forms, respectivel…
23 \begin{aligned} \langle v,u \rangle &:= \int_{\Omega} \, v \, u \, dV ,\\ \langle v,f \rangle &:= \…
30 u(\bm x) &= \sum_{j=1}^n u_j \, \phi_j(\bm x) ,\\
35 The coefficients $\{u_j\}$ and $\{v_i\}$ are the nodal values of $u$ and $v$, respectively.
39 \langle v,u \rangle = \bm v^T M \bm u , \qquad  \langle v,f\rangle =  \bm v^T \bm b \,.
54 …n BP3-BP6 is defined via the following variational formulation, i.e., find $u \in V^p$ such that f…
57 a(v,u) = \langle v,f \rangle , \,
60 where now $a (v,u)$ expresses the continuous bilinear form defined on $V^p$ for sufficiently regula…
63 \begin{aligned} a(v,u) &:= \int_{\Omega}\nabla v \, \cdot \, \nabla u \, dV ,\\ \langle v,f \rangle…
69 a(v,u) = \bm v^T K \bm u ,