[Gmsh] Problem with BSpline, parabolic shape

[Theophile Raux]

Hello!

I am currently using Gmsh to create different simple 2D geometries, such as
squares, circles, etc. The geometry I am working on is a square with a
pseudo-ellipse (2:1 ratio) in its centre. The pseudo-ellipse consists of
two symmetric parabolas. I use parabolas instead of a real ellipse so that
the error of the solution computed by the finite element software is not
due to the spatial discretization.

Anyway, I am using a 2nd order BSpline, with 3 control points and it does
not produce the correct parabola. The parabola's equation is :
-4*x^2 + 4*x -7/16
The BSpline's control points are :
{3/8,1/2,0}, {1/2,5/8,0}, {5/8,1/2,0}

It should produce the same parabola (enclosed is a figure in MATLAB : the
black crosses are the exact parabola, the blue line is the b spline). While
in Gmsh, the BSpline is a bit different from the parabola (enclosed is a
figure in Gmsh).

The figure in Gmsh consists of :
- lines 2,3 : the exact ellipse
- line 1 : the parabola plotted with 101 points and Spline
- line 4 : the parabola plotted with BSpline.

I plotted a parabola using Spline and a zillion collocation points to show
what the parabola in Gmsh should look like. But I can't use this curve in
my program because a spline is a third order curve and the spatial
discretization is not exact.

Thus come my questions : have you come across this problem already ? Do you
know if it's possible to draw an exact parabola in Gmsh using BSpline,
Spline or anything else ? Am I doing something wrong ?

My .geo file is enclosed.

Thank you in advance,

Théophile Raux,
Polytechnique Montréal, CA
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