Consistent and convergent discretizations of Helfrich-type energies on general meshes
Vincent Degrooff and Peter Gladbach and Heiner Olbermann
我们表明,E_0(M)类型表面上的积分曲率能量:= ∫_M f(x,n_M(x),D n_M(x)) dH^2(x)具有三角形复合物的离散版本,其中形状运算符D_M被分段边缘导体的分段梯度所取代。 我们将无 ansatz 的无症状下限结合,用于任何具有三角形复合物的表面的均匀近似值和由极限序列的任何常规三角测量和边缘调节的几乎最佳选择组成的恢复序列。
We show that integral curvature energies on surfaces of the type E_0(M) := ∫_M f(x,n_M(x),D n_M(x)) dℋ^2(x) have discrete versions for triangular complexes, where the shape operator D n_M is replaced by the piecewise gradient of a piecewise affine edge director field. We combine an ansatz-free asymptotic lower bound for any uniform approximation of a surface with triangular complexes and a recovery sequence consisting of any regular triangulation of the limit sequence and an almost optimal choic...
