Source code for FIAT.morley
# Copyright (C) 2008 Robert C. Kirby (Texas Tech University)
#
# This file is part of FIAT (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
from FIAT import finite_element, polynomial_set, dual_set, functional
from FIAT.reference_element import TRIANGLE
[docs]
class MorleyDualSet(dual_set.DualSet):
"""The dual basis for Lagrange elements. This class works for
simplices of any dimension. Nodes are point evaluation at
equispaced points."""
def __init__(self, ref_el):
entity_ids = {}
nodes = []
cur = 0
# make nodes by getting points
# need to do this dimension-by-dimension, facet-by-facet
top = ref_el.get_topology()
verts = ref_el.get_vertices()
if ref_el.get_shape() != TRIANGLE:
raise ValueError("Morley only defined on triangles")
# vertex point evaluations
entity_ids[0] = {}
for v in sorted(top[0]):
nodes.append(functional.PointEvaluation(ref_el, verts[v]))
entity_ids[0][v] = [cur]
cur += 1
# edge dof -- normal at each edge midpoint
entity_ids[1] = {}
for e in sorted(top[1]):
pt = ref_el.make_points(1, e, 2)[0]
n = functional.PointNormalDerivative(ref_el, e, pt)
nodes.append(n)
entity_ids[1][e] = [cur]
cur += 1
entity_ids[2] = {0: []}
super().__init__(nodes, ref_el, entity_ids)
[docs]
class Morley(finite_element.CiarletElement):
"""The Morley finite element."""
def __init__(self, ref_el):
poly_set = polynomial_set.ONPolynomialSet(ref_el, 2)
dual = MorleyDualSet(ref_el)
super().__init__(poly_set, dual, 2)