Merge branch 'fenics_master'

FIAT/expansions.py

@@ -151,7 +151,10 @@ def tabulate_derivatives(self, n, pts):
         tetrahedron expansions."""
         ref_pts = numpy.array([self.mapping(pt) for pt in pts])
         psitilde_as_derivs = jacobi.eval_jacobi_deriv_batch(0, 0, n, ref_pts)
-
+
+        # Jacobi polynomials defined on [-1, 1], first derivatives need scaling
+        psitilde_as_derivs *= 2.0/self.ref_el.volume()
+
         results = numpy.zeros((n+1, len(pts)), "d")
         for k in range(0, n + 1):
             results[k, :] = psitilde_as_derivs[k, :] * numpy.sqrt(k + 0.5)

FIAT/jacobi.py

@@ -104,7 +104,7 @@ def eval_jacobi_deriv_batch(a, b, n, xs):
     else:
         results[1:,:] = eval_jacobi_batch(a+1, b+1, n-1, xs)
     for j in range(1, n+1):
-        results[j,:] *= (a+b+j+1)
+        results[j,:] *= 0.5*(a+b+j+1)
     return results
 
 

FIAT/trace.py

@@ -22,6 +22,7 @@
 from FIAT.discontinuous_lagrange import DiscontinuousLagrange
 from FIAT.reference_element import ufc_simplex
 from FIAT.functional import PointEvaluation
+from FIAT.polynomial_set import mis
 
 # Tolerance for geometry identifications
 epsilon = 1.e-8
@@ -193,8 +194,15 @@ def tabulate(self, order, points):
         """Return tabulated values of derivatives up to given order of
         basis functions at given points."""
 
-        # Standard derivatives don't make sense
-        assert (order == 0), "Don't know how to do derivatives"
+        # Standard derivatives don't make sense, but return zero
+        # because mixed elements compute all derivatives at once
+        if (order > 0):
+            values = {}
+            sdim = self.space_dimension()
+            alphas = mis(self.cell.get_spatial_dimension(), order)
+            for alpha in alphas:
+                values[alpha] = numpy.zeros(shape=(sdim, len(points)))
+            return values
 
         # Identify which facet (if any) these points are on:
         vertices = self.cell.vertices