论文标题
非平滑抛物线偏微分方程的自适应认证时空减少基础方法
An adaptive certified space-time reduced basis method for nonsmooth parabolic partial differential equations
论文作者
论文摘要
在本文中，考虑了非平滑的半线性抛物线偏微分方程（PDE）。为了减少（RB）方法，使用时空公式用于开发经过认证的A-tosteriori误差估计器。该误差估计器被用来存在离散的经验插值方法（DEIM）作为非平滑度的近似技术。然后，估计的误差向RB和Deim部分的可分离性指导自适应RB-DEIM算法的发展，将两个离线阶段组合为一个。与经典的RB和RB-DEIM方法相比，数值实验显示了这种新方法的能力。
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator is adopted to the presence of the discrete empirical interpolation method (DEIM) as approximation technique for the nonsmoothness. The separability of the estimated error into an RB and a DEIM part then guides the development of an adaptive RB-DEIM algorithm, combining both offline phases into one. Numerical experiments show the capabilities of this novel approach in comparison with classical RB and RB-DEIM approaches.
