A reduced-order Weak Galerkin finite element algorithm based on POD technique for parabolic problem on polytopal mesh

Weak Galerkin (WG method) is a numerical method based on the weak functions and weak partial derivatives, which has been widely developed in recent decades. In the implementation, different degrees of freedom (DOFs) are distributed in the element interior and boundary respectively, which leads to a great impact on the computational complexity. In our work, we propose a new reduced-order weak galerkin finite element (RO-WG) method with seldom DOFs, where the proper orthogonal decomposition (POD) technique is adopted to save CPU time. The parabolic equation is considered for a test problem. Some numerical examples are given to prove the superiority of this method, where the CPU time can be reduced a lot.