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DanielDoehring committed Mar 15, 2024
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4 changes: 2 additions & 2 deletions src/solvers/dgsem/basis_lobatto_legendre.jl
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Calculate the barycentric weights for a given node distribution, i.e.,
```math
w_j = \frac{1}{\prod_{k \neq j} \left( x_j - x_k \right )}
w_j = \\frac{1}{ \\prod_{k \\neq j} \\left( x_j - x_k \\right ) }
```
For details, see (especially Section 3)
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This returns all ``l_j(x)``, i.e., the Lagrange polynomials for each node ``x_j``.
Thus, to obtain the interpolating polynomial ``p(x)`` at ``x``, one has to
multiply the Lagrange polynomials with the nodal values ``u_j`` and sum them up:
``p(x) = \sum_{j=1}^{n} u_j l_j(x)``.
``p(x) = \\sum_{j=1}^{n} u_j l_j(x)``.
For details, see e.g. Section 2 of
- Jean-Paul Berrut and Lloyd N. Trefethen (2004).
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