论文标题
Schrödinger方程式
An Ultra-Weak Space-Time Variational Formulation for the Schrödinger Equation
论文作者
论文摘要
我们为线性schrödinger方程的时间依赖性版本提供了一个良好的超湿时时间变异公式，并提供了造型性的哈密顿量。我们证明了最佳的INF-SUP稳定性，并以最佳的离散INF-SUP稳定性引入了时空Petrov-Galerkin化。 我们显示了超弱公式的规范保护。 INF-SUP最佳PETROV-GALERKIL离散化被证明是渐进性的，其中偏差显示为离散化的顺序。此外，我们引入了盖尔金离散化，该离散化具有次优的INF-SUP稳定性但准确的规范保存。 数值实验强调了超湿时时空变异配方的性能，尤其是对于非平滑初始数据。
We present a well-posed ultra-weak space-time variational formulation for the time-dependent version of the linear Schrödinger equation with an instationary Hamiltonian. We prove optimal inf-sup stability and introduce a space-time Petrov-Galerkin discretization with optimal discrete inf-sup stability. We show norm-preservation of the ultra-weak formulation. The inf-sup optimal Petrov-Galerkin discretization is shown to be asymptotically norm-preserving, where the deviation is shown to be in the order of the discretization. In addition, we introduce a Galerkin discretization, which has suboptimal inf-sup stability but exact norm-preservation. Numerical experiments underline the performance of the ultra-weak space-time variational formulation, especially for non-smooth initial data.
