COMSOL Multiphysics™

adaption
fem.bnd.ind = [1 1 2 2 2 2];
fem.solform = 'general';
We refine the elements using the L 2 -norm error estimator, with error minimization
to achieve a factor of 1.3 in each step, and a maximum number of elements of 500.
fem.mesh = meshinit(fem,'hmax',0.3);
fem.xmesh = meshextend(fem);
fem = adaption(fem,'maxt',500,'eefun','fleel2',...
'tpfun','fltpft','tppar',1.3,'report','on');
errexpr = 'abs(u-(x.^2+y.^2).^(1/3).*cos(2/3*atan2(y,x)))';
errmax = postmax(fem,errexpr)
We test how many refinements we have to use with an uniform element net:
tol = errmax;
fem.mesh = meshinit(fem,'hmax',0.3);
fem.xmesh = meshextend(fem);
errmax = 1;
i = 0;
while errmax>tol
fem.sol = femstatic(fem);
errmax = postmax(fem,errexpr);
i = i+1;
fprintf(1,'Refinement:%3d, error:%3.10f, using mesh:\n',...
i,errmax);
fem.mesh
if errmax>tol
fem.mesh = meshrefine(fem);
fem.xmesh = meshextend(fem);
end
end
Note that with uniform refinement, you need much more mesh elements to achieve
the same absolute error as with the adaptive method. Also note that the error is
reduced only by a small factor when the number of elements is quadrupled by the
uniform refinement. For a problem with regular solution, you can expect a O(h 2 )
error, but this solution is singular because u ≈ r 1/3 at the origin.
Eigenmodes of a Nonconvex Geometry
Solve the eigenvalue problem
⎧
⎨
⎩
– ∇ ⋅ ∇u
= λu in Ω
u = 0
on ∂Ω
,
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