add bubble element

Author: mscroggs

symfem/__init__.py

@@ -91,7 +91,7 @@ def create_element(cell_type, element_type, order):
                           Nedelec2, N2curl, Raviart-Thomas, RT, N1div, dQ, NCE, RTCE,
                           Qcurl, Q, NCF, RTCF, Qdiv, vector Q, vQ,
                           Brezzi-Douglas-Marini, BDM, N2div, Morley, Hermite,
-                          Mardal-Tai-Winther, MTW, Argyris
+                          Mardal-Tai-Winther, MTW, Argyris, bubble
     order : int
         The order of the element.
     """

symfem/elements/bubble.py

@@ -0,0 +1,41 @@
+"""Bubble elements on simplices."""
+
+import sympy
+from itertools import product
+from ..core.symbolic import x
+from ..core.finite_element import FiniteElement
+from ..core.polynomials import polynomial_set
+from ..core.functionals import PointEvaluation
+
+
+class Bubble(FiniteElement):
+    """Bubble finite element."""
+
+    def __init__(self, reference, order):
+        if reference.name == "interval":
+            poly = [x[0] * (1 - x[0]) * p for p in polynomial_set(reference.tdim, 1, order - 2)]
+        elif reference.name == "triangle":
+            poly = [x[0] * x[1] * (1 - x[0] - x[1]) * p
+                    for p in polynomial_set(reference.tdim, 1, order - 3)]
+        else:
+            assert reference.name == "tetrahedron"
+            poly = [x[0] * x[1] * x[2] * (1 - x[0] - x[1] - x[2]) * p
+                    for p in polynomial_set(reference.tdim, 1, order - 4)]
+
+        dofs = []
+        for i in product(range(1, order), repeat=reference.tdim):
+            if sum(i) < order:
+                dofs.append(
+                    PointEvaluation(
+                        tuple(o + sum(sympy.Rational(a[j] * b, order)
+                                      for a, b in zip(reference.axes, i))
+                              for j, o in enumerate(reference.origin)),
+                        entity_dim=reference.tdim))
+
+        super().__init__(
+            reference, poly, dofs, reference.tdim, 1
+        )
+
+    names = ["bubble"]
+    references = ["interval", "triangle", "tetrahedron"]
+    min_order = {"interval": 2, "triangle": 3, "tetrahedron": 4}

test/test_all_elements.py

@@ -13,10 +13,20 @@ def handler(signum, frame):
 
 elements = []
 for e in _elementlist:
-    min_o = e.min_order if hasattr(e, "min_order") else 0
-    max_o = min(5, e.max_order) if hasattr(e, "max_order") else 5
     for r in e.references:
-        for order in range(min_o, max_o + 1):
+        if hasattr(e, "min_order"):
+            min_o = e.min_order
+            if isinstance(min_o, dict):
+                min_o = min_o[r]
+        else:
+            min_o = 0
+        if hasattr(e, "max_order"):
+            max_o = e.max_order
+            if isinstance(max_o, dict):
+                max_o = max_o[r]
+        else:
+            max_o = 100
+        for order in range(min_o, min(5, max_o) + 1):
             elements.append((r, e.names[0], order))