Test shapefunction duality

Previously, the testLocalInterpolation method constructed random linear combinations of the shape functions, and then checked whether the 'interpolate' method would recover the random coefficients. This patch rewrites the test to call 'interpolate' on the individual shape functions, and check whether the resulting coefficient set is the correct unit vector. While this does not really result in an increase of test coverage, it puts the test more in line with the classic Ciarlet definition of a (local) finite element. There, the shape functions are defined as the dual basis to the set of degrees of freedom, and the new test tests this directly. It also is a bit shorter, too.

First of all: I like the new test.

But I'm not sure if it's sufficient. By considering random linear combinations of basis functions we somehow also check if the interpolation is linear (otherwise being correct is hardly possible). However, this concern is maybe academic because it's unlikely that an interpolation bug preserves duality but not linearity.

You are right, linearity is a defining property of degrees of freedom, and it is not currently tested. Should we have a separate test that explicitly tests linearity?

I think so. In order to avoid falling into special cases, this should perhaps again be randomized (using a fixed seed of course).

mentioned in issue infrastructure/releases#1

changed milestone to %DUNE 2.6.0

merged

mentioned in commit adb16631

mentioned in commit 24fa4925

mentioned in merge request !84 (merged)