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Cyclotourist (talk | contribs) |
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*<math>\nabla_D u = \sum_{i\in I} u_i \nabla\psi_i.</math>
In this case, <math>C_D</math> is the constant involved in the continuous Poincaré inequality, and, for all <math>\varphi\in H_\operatorname{div}(\Omega)</math>, <math>W_{D}(\varphi) = 0</math> (defined by (8)). Then (4) and (5) are implied by [[Céa's lemma]].
The "mass-lumped" <math>P^1</math> finite element case enters the framework of the GDM, replacing <math>\Pi_D u</math> by <math>\widetilde{\Pi}_D u = \sum_{i\in I} u_i \chi_{\Omega_i}</math>, where <math>\Omega_i</math> is a dual cell centred on the vertex indexed by <math>i\in I</math>. Using mass lumping allows to get the piecewise constant reconstruction property.
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