A-posteriori error analysis for a staggered discontinuous Galerkin discretization of the time-harmonic Maxwell’s equations

Chung, Eric T.; Yuen, Man Chun; Zhong, Liuqiang

doi:10.1016/j.amc.2014.03.134

Cited by 8 publications

(2 citation statements)

References 27 publications

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“…Recently, a new class of staggered DG (SDG) methods based on staggered meshes was proposed and analyzed. In particular, the SDG method has been successfully developed for many wave propagation problems Engquist, 2006, 2009;Chung and Lee, 2012;Chan et al, 2013;Chung and Ciarlet, 2013;Chung et al, 2013a) and other applications (Chung et al, 2013b(Chung et al, , 2014a(Chung et al, , 2014bKim et al, 2013Kim et al, , 2014Chung and Kim, 2014). The SDG method is typically applied to the first-order formulation of wave equations, and it starts with two sets of irregular, staggered grids for each of the two unknown functions involved; furthermore, it designs two finite-element spaces on those two sets of staggered grids and carries out integration-by-parts to derive corresponding weak formulations; and finally, it applies the standard leap-frog scheme for explicit time stepping.…”

Section: Introductionmentioning

confidence: 99%

A staggered discontinuous Galerkin method for the simulation of seismic waves with surface topography

2015

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Accurate simulation of seismic waves is of critical importance in a variety of geophysical applications. Based on recent works on staggered discontinuous Galerkin methods, we have developed a new method for the simulations of seismic waves, which has energy conservation and extremely low grid dispersion, so that it naturally provided accurate numerical simulations of wave propagation useful for geophysical applications and was a generalization of classical staggered-grid finite-difference methods. Moreover, it could handle with ease irregular surface topography and discontinuities in the subsurface models. Our new method discretized the velocity and the stress tensor on this staggered grid, with continuity imposed on different parts of the mesh. The symmetry of the stress tensor was enforced by the Lagrange multiplier technique. The resulting method was an explicit scheme, requiring the solutions of a block diagonal system and a local saddle point system in each time step, and it was, therefore, very efficient. To tailor our scheme to Rayleigh waves, we developed a mortar formulation of our method. Specifically, a fine mesh was used near the free surface and a coarse mesh was used in the rest of the domain. The two meshes were in general not matching, and the continuity of the velocity at the interface was enforced by a Lagrange multiplier. The resulting method was also efficient in time marching. We also developed a stability analysis of the scheme and an explicit bound for the time step size. In addition, we evaluated some numerical results and found that our method was able to preserve the wave energy and accurately computed the Rayleigh waves. Moreover, the mortar formulation gave a significant speed up compared with the use of a uniform fine mesh, and provided an efficient tool for the simulation of Rayleigh waves.

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Section: Introductionmentioning

confidence: 99%

A staggered discontinuous Galerkin method for the simulation of seismic waves with surface topography

2015

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“…For example, DG methods allow more fexibility in handling equations whose types change within the computational domain and the corresponding finite element space has no continuity constraints across the edges/faces of the triangulation. Because of these advantages, DG methods are extended to various model problems, such as elliptic problems [1], Navier-Stokes equations [2], Maxwell equations [5] and so on. Recent years, some different types of DG methods have been developed, such as the symmetric interior penalty discontinuous Galerkin (SIPDG) method [13], incomplete interior penalty discontinuous Galerkin (IIPDG) method [12], local DG method [7] and so on.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Galerkin methods for semilinear elliptic boundary value problem

Jin¹,

Zhong²,

Peng³

2021

Preprint

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A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretizations are established, and the corresponding existence and uniqueness theorem is proved by using Brouwer's fixed point method. Some optimal priori error estimates under both DG norm and L 2 norm are presented. Numerical results are also shown to confirm the efficiency of the proposed approach.

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An Adaptive SDG Method for the Stokes System

Chung

Yuen

2016

J Sci Comput

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A-posteriori error analysis for a staggered discontinuous Galerkin discretization of the time-harmonic Maxwell’s equations

Cited by 8 publications

References 27 publications

A staggered discontinuous Galerkin method for the simulation of seismic waves with surface topography

A staggered discontinuous Galerkin method for the simulation of seismic waves with surface topography

Discontinuous Galerkin methods for semilinear elliptic boundary value problem

An Adaptive SDG Method for the Stokes System

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