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Copy file name to clipboardExpand all lines: chapter1/fundamentals.md
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@@ -107,7 +107,7 @@ The variational problem is a _continuous problem_: it defines the solution $u$ i
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The finite element method for the Poisson equation finds an approximate solution of the variational problem by replacing the infinite-dimensional function spaces $V$ and $\hat{V}$ by _discrete_ (finite dimensional) trial and test spaces $V_h\subset V$ and $\hat{V}_h \subset \hat{V}$. The discrete
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variational problem reads: Find $u_h\in V_h$ such that
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\begin{align}
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\int_\Omega \nabla u_h \cdot \nabla v~\mathrm{d} x &= \int_\Omega fv~\mathrm{d} x && \forall v \in \hat{V}\_h.
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\int_\Omega \nabla u_h \cdot \nabla v~\mathrm{d} x &= \int_\Omega fv~\mathrm{d} x && \forall v \in \hat{V}_h.
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\end{align}
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This variational problem, together with suitable definitions of $V_h$ and $\hat{V}_h$ uniquely define our approximate numerical solution of the Poisson equation.
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Note that the boundary condition is encoded as part of the test and trial spaces. This might seem complicated at first glance,
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