[CIG-CS] Particle problems and Semi-Lagrangian Schemes for Gamr

[Walter Landry]

Wolfgang Bangerth <bangerth at math.tamu.edu> wrote:
> In your original mail, you had this statement:
> 
>> Because of the higher order Q2 elements, it takes
>> literally hundreds of particles to get a solution accurate to a part
>> in 10^3 in 2D.
> 
> Do you mean hundreds of particles *per cell*? And what is the measure by
> which you compute accuracy?

Yes, per cell.  The test problem I used was pure shear in a box.  The
boundary conditions are

      __________
     |          |
vx=0 |          |  vx=1
     |          |
     |          |
     |__________|

        vy=0

Everything else is unspecified.  It is a single Q2-Q1 element.  For
the accuracy, I know what the velocities at the nodal points should be
(e.g. 1/2) and I compared them directly to the computed value.  It
required 140 particles to get an error of 10^-3 in the velocity.

In contrast, for the same problem using a Q1-Q1 element, it only
requires 7 particles.

Luke Hodkinson at VPAC told me a few years ago that he had seen the
same result.

Cheers,
Walter Landry
walter at geodynamics.org