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.

在本文中，考虑非光滑半线性抛物型偏微分方程（PDE）。对于简化基（RB）方法，时空公式用于开发经过认证的后验误差估计器。该误差估计器采用离散经验插值法（DEIM）作为非平滑性的近似技术。然后，估计误差可分为 RB 和 DEIM 部分，从而指导自适应 RB-DEIM 算法的开发，将两个离线阶段合并为一个。数值实验显示了这种新方法与经典 RB 和 RB-DEIM 方法相比的能力。