A New Ensemble HDG Method for Parameterized Convection Diffusion PDEs

Abstract

A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions, body forces, and time depending coefficients is developed. For ensemble solutions in L ∞ (0, T ; L 2 (Ω)), a superconvergent rate with respect to the freedom degree of the globally coupled unknowns for all the polynomials of degree k ≥ 0 is established. The results of numerical experiments are consistent with the theoretical findings.

Convergence Analysis and Cost Estimate of an MLMC-HDG Method for Elliptic PDEs with Random Coefficients

“…Similar to the standard finite element, the computational cost of the HDG method is of linear complexity in the number N l on every sub-level l (see, e.g., [24]). For M l samples, the cost is O(M l • N l ).…”

A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem

“…Moreover, an optimal $$$ {L}^2 $$$ convergence rate was obtained for the ensemble solutions. In [37], a second‐order time stepping ensemble HDG scheme also was given to get a super‐convergent accuracy. However, to our knowledge there is no research on HDG method for second‐order parabolic PDEs with random coefficients.…”