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We devised a first order time stepping ensemble hybridizable discontinuousGalerkin (HDG) method for a group of parameterized convection diffusion PDEswith different initial conditions, body forces, boundary conditions andcoefficients in our earlier work [3]. We obtained an optimal convergence ratefor the ensemble solutions in $L^\infty(0,T;L^2(\Omega))$ on a simplex mesh;and obtained a superconvergent rate for the ensemble solutions in$L^2(0,T;L^2(\Omega))$ after an element-by-element postprocessing ifpolynomials degree $k\ge 1$ and the coefficients of the PDEs are independent oftime. In this work, we propose a new second order time stepping ensemble HDGmethod to revisit the problem. We obtain a superconvergent rate for theensemble solutions in $L^\infty(0,T;L^2(\Omega))$ without an element-by-elementpostprocessing for all polynomials degree $k\ge 0$. Furthermore, our mesh canbe any polyhedron, no need to be simplex; and the coefficients of the PDEs candependent on time. Finally, we present numerical experiments to confirm ourtheoretical results.

A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs