A FEniCS Tutorial - FEniCS Project

Other functions for visualizing 2D scalar fields are surf and mesh as known
from MATLAB:
import scitools.easyviz as ev
ev.figure()
ev.surf(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values,
shading=’interp’, colorbar=’on’,
title=’surf plot of u’, savefig=’u_surf.eps’)
ev.figure()
ev.mesh(u_box.grid.coorv[X], u_box.grid.coorv[Y], u_box.values,
title=’mesh plot of u’, savefig=’u_mesh.eps’)
Figure 1.12 exemplifies the surfaces arising from the two plotting commands
above. You can type pydoc scitools.easyviz in a terminal window to get
a full tutorial. Note that scitools.easyviz offers function names like plot
and mesh, which clash with plot from dolfin and the mesh variable in our
programs. Therefore, we recommend the ev prefix.
A handy feature of BoxField is the ability to give a start point in the grid
and a direction, and then extract the field and corresponding coordinates along
the nearest grid line. In 3D fields one can also extract data in a plane. Say we
want to plot u along the line y = 1/2 in the grid. The grid points, x, and the u
values along this line, uval, are extracted by
start = (0, 0.5)
x, uval, y_fixed, snapped = u_box.gridline(start, direction=X)
The variable snapped is true if the line had to be snapped onto a gridline and
in that case y_fixed holds the snapped (altered) y value. Plotting u versus the
x coordinate along this line, using scitools.easyviz, is now a matter of
ev.figure() # new plot window
ev.plot(x, uval, ’r-’) # ’r--: red solid line
ev.title(’Solution’)
ev.legend(’finite element solution’)
# or more compactly:
ev.plot(x, uval, ’r-’, title=’Solution’,
legend=’finite element solution’)
A more exciting plot compares the projected numerical flux in x direction
along the line y = 1/2 with the exact flux:
ev.figure()
flux2_x = flux_x if flux_x.ufl_element().degree() == 1 else \
interpolate(flux_x, FunctionSpace(mesh, ’Lagrange’, 1))
flux_x_box = scitools.BoxField.dolfin_function2BoxField(
flux2_x, mesh, (nx,ny), uniform_mesh=True)
x, fluxval, y_fixed, snapped = \
flux_x_box.gridline(start, direction=X)
y = y_fixed
flux_x_exact = -(x + y)*2*x
ev.plot(x, fluxval, ’r-’,
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