I implemented an exact solution for the mean curvature for ellipsoids
(it's a slightly ugly expression, I just took it from
here: http://math.stackexchange.com/a/540820), and I computed the L2 and
Linfty errors between my computed values and that expression. The
result: Convergence wrt mesh ref
On Tuesday, August 23, 2016 at 12:51:53 PM UTC-4, Wolfgang Bangerth wrote:
>
>
> Thomas,
>
> > I was able to solve for the vector mean curvature using the weak form of
> > the identity k_bar = laplacian_X id_X, where X is a codimension 1
> > manifold without boundary. The image above is a plo
Thomas,
I was able to solve for the vector mean curvature using the weak form of
the identity k_bar = laplacian_X id_X, where X is a codimension 1
manifold without boundary. The image above is a plot of the square of
the mean curvature on an ellipsoid with semi principle axes a=1,b=2,c=3.
Gr
On 08/19/2016 01:15 PM, thomas stephens wrote:
Wolfgang, I appreciate your assistance so far.
I'm getting closer, but I still need some help. I would like to look at this
problem as it appears in [1], Equation 27 on p. 11, as the bilinear forms are
written as integrals, making things more clear
Wolfgang, I appreciate your assistance so far.
I'm getting closer, but I still need some help. I would like to look at
this problem as it appears in [1], Equation 27 on p. 11, as the bilinear
forms are written as integrals, making things more clear.
Below I have set up what I think to be the
On 08/18/2016 09:39 AM, thomas stephens wrote:
id_X looks like this:
|
template
classIdentity:publicFunction
{
public:
Identity():Function(){}
virtualvoidvector_value(constPoint&p,Vector&value)const;
virtualdoublevalue(constPoint&p,constunsignedintcomponent
=0)const;
};
Identityid_X
id_X looks like this:
template
class Identity: public Function
{
public:
Identity() : Function() {}
virtual void vector_value(const Point &p, Vector &
value) const;
virtual double value(const Point &p, const unsigned int
component = 0) const;
};
Identity id_X();
Do I need to
On 08/17/2016 10:22 AM, thomas stephens wrote:
*On to the question: *It is a fact that the vector mean curvature k_bar
is equal to the surface laplacian of the identity function id_X on the
manifold X, k_bar = laplace_beltrami id_X. Equation (4.4) in [1] is
the weak form of this identity: (k_b
