Discontinuous Galerkin method in numerical simulation of two-dimensional thermoelasticity problem with single stabilization parameter

Jaśkowiec, Jan; Pluciński, Piotr

doi:10.1016/j.advengsoft.2018.04.015

Cited by 3 publications

(3 citation statements)

References 49 publications

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“…1 b, where the trial function or its derivatives should be calculated to evaluate the numerical fluxes. It has been shown in other papers, for example 3 – 5 , 63 , that the DGFD method is stable and not sensitive to fluctuations of . A wider discussion of parameter is presented in “ Discussion on the stability parameter ” Section.…”

Section: Problem Formulationmentioning

confidence: 88%

“…The parameter measures the small distance from the mesh skeleton, so its value depends on the size of the adjacent elements. On the other hand, its value is independent of the considered problem, but has to be adjusted to the mesh, so it is possible to use a single stabilization parameter for coupled problems 63 . The parameter cannot be arbitrarily small since numerical instabilities can occur if it is too small.…”

Section: Discussion On the Stability Parametermentioning

confidence: 99%

“…The parameter is related only to the mesh, not to the considered problem. Therefore, different types of boundary problems can be solved using the same mesh with a similar value of the stability parameter 63 . The numerical fluxes on the mesh skeleton are evaluated using finite difference formulas in the small neighborhood of the mesh skeleton which is defined by parameter 3 .…”

Section: Problem Formulationmentioning

confidence: 99%

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A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems

Jaśkowiec

Pamin

2023

Sci Rep

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The paper presents a posteriori error approximation concept based on residuals in the two-dimensional discontinuous Galerkin (DG) method. The approach is relatively simple and effective in application, and it takes advantage of some unique properties of the DG method. The error function is constructed in an enriched approximation space, utilizing the hierarchical nature of the basis functions. Among many versions of the DG method, the most popular one is based on the interior penalty approach. However, in this paper a DG method with finite difference (DGFD) is utilized, where the continuity of the approximate solution is enforced by finite difference conditions applied on the mesh skeleton. In the DG methods arbitrarily shaped finite elements can be used, so in this paper the meshes with polygonal finite elements are considered, including quadrilateral and triangular elements. Some benchmark examples are presented, in which Poisson’s and linear elasticity problems are considered. The examples use various mesh densities and approximation orders to evaluate the errors. The error estimation maps, generated for the discussed tests, indicate a good correlation with the exact errors. In the last example, the error approximation concept is applied for an adaptive hp mesh refinement.

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Section: Problem Formulationmentioning

confidence: 88%

Section: Discussion On the Stability Parametermentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

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A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems

Jaśkowiec

Pamin

2023

Sci Rep

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Solving of multi-connected curvilinear boundary value problems by the fast PIES

Kużelewski

Zieniuk

2022

Computer Methods in Applied Mechanics and Engineering

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A Robust Discontinuous Galerkin High-Order Finite Element Method for Elasticity Problems with Interfaces

Zhang

Deng

2019

Int. J. Comput. Methods

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A robust discontinuous Galerkin (DG) finite element method is proposed for elasticity problems with interfaces, where the continuity across the interfaces is weakly enforced by using Nitsche’s method. We employ a weighting for the interfacial consistency terms arising in the Nitsche variational form and present a detailed finite element formulation of this DG method. The stabilization parameter is evaluated by solving element level generalized eigenvalue problem for higher-order elements. Consequently, we give the choice of the weighting parameter that results in an estimate for the stabilization parameter such that the method remains well behaved in the pathological cases. The accuracy and robustness of the proposed method are then demonstrated through several numerical examples.

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Discontinuous Galerkin method in numerical simulation of two-dimensional thermoelasticity problem with single stabilization parameter

Cited by 3 publications

References 49 publications

A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems

A posteriori error approximation in discontinuous Galerkin method on polygonal meshes in elliptic problems

Solving of multi-connected curvilinear boundary value problems by the fast PIES

A Robust Discontinuous Galerkin High-Order Finite Element Method for Elasticity Problems with Interfaces

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