A reduced-order discontinuous Galerkin method based on a Krylov subspace technique in nanophotonics

Li, Kun; Huang, Ting‐Zhu; Li, Liang; Lanteri, Stéphane

doi:10.1016/j.amc.2019.04.031

Cited by 2 publications

(1 citation statement)

References 32 publications

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“…On the other hand, for velocity and pressure approximation, the discontinuous Galerkin formulation with P 1 − P 0 space is stable [85]. Because of its flexibility for mesh/polynomial refinement, localizability, and stability, the discontinuous Galerkin method has been widely extended and applied to solve many partial differential equations, such as the local discontinuous Galerkin (LDG) method [17,22,51,97], the interior penalty discontinuous Galerkin (IPDG) method [1,24,25,78,86,96,101], the hybridizable DG method [10,20,43,48,76], reduced order DG method [58][59][60], and many others [15, 49, 61, 68, 72-74, 81, 92, 95, 108]. One important feature of the IPDG method is its capability to easily incorporate hp local refinement.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model

Gao

Chen

et al. 2020

Adv Comput Math

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In this paper, we propose a discontinuous finite volume element method to solve a phase field model for two immiscible incompressible fluids. In this finite volume element scheme, discontinuous linear finite element basis functions are used to approximate the velocity, phase function, and chemical potential while piecewise constants are used to approximate the pressure. This numerical method is efficient, optimally convergent, conserving the mass, convenient to implement, flexible for mesh refinement, and easy to handle complex geometries with different types of boundary conditions. We rigorously prove the mass conservation property and the discrete energy dissipation for the proposed fully discrete discontinuous finite volume element scheme. Using numerical tests, we verify the accuracy, confirm the mass conservation and the energy law, test the influence of surface tension and small density variations, and simulate the driven cavity, the Rayleigh-Taylor instability.

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