ffc team mailing list archive

[Matthew Knepley <knepley@xxxxxxxxxxx>]

Isn't this strange since the error bounds no longer apply outside the
element
(it is no longer interpolation, but extrapolation)?

  Matt

On Wed, Sep 16, 2009 at 8:59 AM, Anders Logg <logg@xxxxxxxxx> wrote:

> Marie and I came across a "bug" when trying to use evaluate_basis in a
> way it was probably not intended for.
>
> In particular, we want to evaluate the basis functions for a cell in a
> point that lies outside the cell. This fails when we evaluate the
> basis functions in a point where the collapsing square map in FIAT is
> singular.
>
> Here's a simple script that illustrates the problem:
>
>  from dolfin import *
>  import numpy
>
>  mesh = UnitSquare(1, 1, "left")
>  V = FunctionSpace(mesh, "CG", 1)
>  element = V.dolfin_element()
>  cell = Cell(mesh, 0)
>  value = numpy.zeros(1)
>
>  # Value should be 1.0 (constant along x = 1)
>  element.evaluate_basis(1, value, numpy.array((1.0, 1.0000000000001)),
> cell)
>  print value
>
>  # Should also be 1.0 but result is 0 (eps)
>  element.evaluate_basis(1, value, numpy.array((1.0, 1.0000000000000)),
> cell)
>  print value
>
> The problem is the following lines in evaluate_basis:
>
>  // Map coordinates to the reference square
>  if (std::abs(y - 1.0) < 1e-14)
>    x = -1.0;
>  else
>    x = 2.0 *x/(1.0 - y) - 1.0;
>  y = 2.0*y - 1.0;
>
> In the above example, y = 1 so x is mapped to -1.0 on Rob's reference
> square.
>
> Is there a simple fix that would allow us to evaluate the basis
> functions outside the element?
>
> --
> Anders
>
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What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments
lead.
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