Lagrange_and_edge_polynomials.py¶
Lagrange polynomials and edge polynomials in the 1d reference element .
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- Lagrange_and_edge_polynomials.Lagrange_polynomials(nodes, xi)[source]¶
Compute the Lagrange polynomials built on
nodes
. They are then evaluated atxi
.- Parameters:
nodes (1d np.array) – The nodes on which the Lagrange polynomials are built.
xi (1d np.array) – The points to evaluate the Lagrange polynomials.
- Returns:
A 2d numpy.array whose 0-dimension refers to the indexes of the polynomials and 1-dimension refers to the values evaluated at
xi
.- Example:
>>> nodes = np.array([-1., -0.4472136, 0.4472136, 1.]) >>> x = np.linspace(-1, 1, 50) >>> lp = Lagrange_polynomials(nodes, x) >>> lp[0,:] # l^0(xi) array([ 1. , 0.88167345, 0.77142177, 0.66898996,...
- Lagrange_and_edge_polynomials.edge_polynomials(nodes, xi)[source]¶
Compute the edge polynomials built on
nodes
. They are then evaluated atxi
.- Parameters:
nodes (1d np.array) – The nodes on which the edge polynomials are built.
xi (1d np.array) – The points to evaluate the edge polynomials.
- Returns:
A 2d numpy.array whose 0-dimension refers to the indexes of the polynomials and 1-dimension refers to the values evaluated at
xi
.- Example:
>>> nodes = np.array([-1., -0.65465367, 0., 0.65465367, 1.]) >>> x = np.linspace(-1, 1, 50) >>> ep = edge_polynomials(nodes, x) >>> ep[2,:] # e^3(xi) array([ 0.91016418, 0.60853048, 0.34702611, 0.12374712, ...
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