Page 384 - Process Modelling and Simulation With Finite Element Methods

A MATLAB/FEMLAB Primer for Vector Calculus 37 1

Clearly, for such a coarse mesh, half a percent error is not a bad result. Now for
the curl.
>>xxx= LO. 42; 0.57; 0.331 ; [postinterp (fern, 'u3y-u2z' ,xxx) ;
postinterp(fem,' ulz-u3x',xxx);postinterp(fem,'u2x-~iy',xxx)]
ans =
0.0043
-0.5319
1.7100
>> [O; -3*0.42A2; 3*0.57]
ans =
0
-0.5292
1.7100
The worst error here is again half a percent.

Figure A6. Isosurfaces of divergence computed for the example F = (X', 3Xy, X' )

Figure A6 shows the numerical approximation by FEM to the divergence, which
qualitatively shows isosurfaces consistent with v . F = 5x. Figure A1 shows
the arrow plot of curl F. Since most of us have little feel for three-dimensional
vector plots, determining whether the plot is consistent with the closed form
calculation is beyond our visual capacity for numeracy. Nevertheless, the FEM
solution shows the very important feature of numerical solutions - visualization
of solutions. Does anyone have a feel for the analytic solution
v X F = (0, -3x2, 3y) either?