Add feec docs#380
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| * $l(v) = \int_\Omega f v \, dx$ is a linear form. | ||
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| This formulation requires $u$ and $v$ to only have (square-integrable) first derivatives and thus describes a much larger class of situations than the strong form. | ||
| For instance, the graph of the solution for a discontinuous choice of $f$ on a square domain is shown below: |
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Seems like there is a figure missing?
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| Such a discretization fails on the L-shaped domain: the discrete solution lives in a proper closed subspace of ``H(\text{curl}; \Omega) \cap \mathring{H}(\text{div}; \Omega)``, producing spurious modes that persist under mesh refinement. | ||
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The figure should be a tad smaller.
| The spaces ``V_h^0`` and ``V_h^1`` need to be chosen in a "compatible" manner (in the sense described in the following sections), but when they are, the discrete solution converges to the true solution, and we avoid the issues associated with the primal formulation. | ||
| Note that this is true even when ``V_h^1`` is an appropriately chosen ``H^1``-conforming space (e.g., that of ``C^1`` smooth B-spline edge elements): the key difference from the primal formulation is that now the ``H(\text{curl};\Omega)``-norm restricted to such spaces is not equivalent to the ``H^1`` norm. | ||
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