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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.25 No.3
- 발행연도
- 2021.9
- 수록면
- 66 - 81 (16page)
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In this paper, we review the lowest order staggered discontinuous Galerkin methods on polygonal meshes in 2D. The proposed method offers many desirable features including easy implementation, geometrical flexibility, robustness with respect to mesh distortion and low degrees of freedom. Discrete function spaces for locally H¹ and H(div) spaces are considered. We introduce special properties of a sub-mesh from a given star-shaped polygonal mesh which can be utilized in the construction of discrete spaces and implementation of the staggered discontinuous Galerkin method. For demonstration purposes, we consider the lowest case for the Poisson equation. We emphasize its efficient computational implementation using only geometrical properties of the underlying mesh.
목차
ABSTRACT
1. INTRODUCTION
2. POLYGONAL MESHES AND STAGGERED MESHES
3. PIECEWISE CONFORMING DISCRETE SPACES
4. POISSON EQUATION
5. NUMERICAL EXPERIMENTS
6. CONCLUSION
REFERENCES
참고문헌 (30)
참고문헌 신청
E.L. Wachspress / 1975 / A Rational Finite Element Basis / Academic Press
L. Beirao da Veiga / 2013 / ˜ Basic principles of virtual element methods / Mathematical Models and Methods in Applied Sciences 23:199~214
L. Beirao da Veiga / 2014 / The Hitchhiker’s Guide to the Virtual Element Method / Mathematical Models and Methods in Applied Sciences 24:1541~1573
D. A. Di Pietro / 2014 / An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators / Computational Methods in Applied Mathematics 14:461~472
D. A. Di Pietro / 2020 / The hybrid high-order method for polytopal meshes / Springer International Publishing
L. Beirao da Veiga / 2013 / ˜ Basic principles of virtual element methods / Mathematical Models and Methods in Applied Sciences 23:199~214
L. Beirao da Veiga / 2014 / The Hitchhiker’s Guide to the Virtual Element Method / Mathematical Models and Methods in Applied Sciences 24:1541~1573
D. A. Di Pietro / 2014 / An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators / Computational Methods in Applied Mathematics 14:461~472
D. A. Di Pietro / 2020 / The hybrid high-order method for polytopal meshes / Springer International Publishing
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