Lines Matching +full:- +full:f

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10 (mass-operator)=
17 \langle v,u \rangle = \langle v,f \rangle ,
18 $$ (eq-general-weak-form)
20 …ngle v,f\rangle$ express the continuous bilinear and linear forms, respectively, defined on $V^p$,…
23 …u \rangle &:= \int_{\Omega} \, v \, u \, dV ,\\ \langle v,f \rangle &:= \int_{\Omega} \, v \, f \,…
33 $$ (eq-nodal-values)
36 Inserting the expressions {eq}`eq-nodal-values` into {eq}`eq-general-weak-form`, we obtain the inne…
39 \langle v,u \rangle = \bm v^T M \bm u , \qquad  \langle v,f\rangle =  \bm v^T \bm b \,.
40 $$ (eq-inner-prods)
42 Here, we have introduced the mass matrix, $M$, and the right-hand side, $\bm b$,
45 M_{ij} :=  (\phi_i,\phi_j), \;\; \qquad b_{i} :=  \langle \phi_i, f \rangle,
50 (laplace-operator)=
54 The Laplace's operator used in BP3-BP6 is defined via the following variational formulation, i.e., …
57 a(v,u) = \langle v,f \rangle , \,
60 … the continuous bilinear form defined on $V^p$ for sufficiently regular $u$, $v$, and $f$, that is:
63 …{\Omega}\nabla v \, \cdot \, \nabla u \, dV ,\\ \langle v,f \rangle &:= \int_{\Omega} \, v \, f \,…
66 After substituting the same formulations provided in {eq}`eq-nodal-values`, we obtain