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The finite element method is a popular method for approximating numerically on a computer the solution of partial differential equations. It is based on a variational (weak) formulation of the PDE, followed by discretization on a finite-dimensional ansatz space which reduces the problem to a sparse linear algebra one.

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Finite element method inverse estimate

You may take a look at Theorem 3.2.6 p140 in the book Philippe G. Ciarlet, The Finite Element Method for Elliptic Problems.
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