论文标题
校正：随机总变化流的收敛数值近似
Correction to: Convergent numerical approximation of the stochastic total variation flow
论文作者
论文摘要
我们在论文中纠正两个错误[4]。第一个错误涉及SVI解决方案的定义，其中不包括由于Dirichlet边界条件而产生的边界项。第二个错误涉及离散估计[4，引理4.4]，该估计涉及离散的拉普拉斯操作员。我们通过使用离散的laplacian的质量大型版本提供了空间维度$ d = 1 $估算的替代证明。因此，在对完全离散的数值方案进行了较小的修改后，$ d = 1 $的收敛遵循原始证明的行。时间半混凝土方案的收敛证明依赖于估计值的连续对应[4，引理4.4]，在较高的空间尺寸中仍然有效。 [3]中通过使用不同的方法显示了[4]中[4]中完全离散的有限元方案的收敛。
We correct two errors in our paper [4]. First error concerns the definition of the SVI solution, where a boundary term which arises due to the Dirichlet boundary condition, was not included. The second error concerns the discrete estimate [4, Lemma 4.4], which involves the discrete Laplace operator. We provide an alternative proof of the estimate in spatial dimension $d=1$ by using a mass lumped version of the discrete Laplacian. Hence, after a minor modification of the fully discrete numerical scheme the convergence in $d=1$ follows along the lines of the original proof. The convergence proof of the time semi-discrete scheme, which relies on the continuous counterpart of the estimate [4, Lemma 4.4], remains valid in higher spatial dimension. The convergence of the fully discrete finite element scheme from [4] in any spatial dimension is shown in [3] by using a different approach.
