과제정보
The research of EJP was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021).
참고문헌
- E.L. Wachspress, A Rational Finite Element Basis, Academic Press, New York, New York, 1975.
- L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini and A. Russo, Basic principles of virtual element methods, Mathematical Models and Methods in Applied Sciences, 23 (2013), 199-214. https://doi.org/10.1142/S0218202512500492
- L. Beirao da Veiga, F. Brezzi, L. D. Marini and A. Russo The Hitchhiker's Guide to the Virtual Element Method, Mathematical Models and Methods in Applied Sciences, 24 (2014), 1541-1573. https://doi.org/10.1142/S021820251440003X
- D. A. Di Pietro, A. Ern and S. Lemaire, An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators, Computational Methods in Applied Mathematics, 14 (2014), 461-472. https://doi.org/10.1515/cmam-2014-0018
- D. A. Di Pietro and J. Droniou, The hybrid high-order method for polytopal meshes, Springer International Publishing, 2020.
- F. Bassi, L. Botti, A. Colombo, D. A. Di Pietro and P. Tesini, On the flexibility of agglomeration-based physical space discontinuous Galerkin discretizations, Journal of Compututational Physics, 231 (2012), 45-65. https://doi.org/10.1016/j.jcp.2011.08.018
- P. F. Antonietti, S. Giani and P. Houston, hp-version composite discontinuous Galerkin methods for elliptic problems on complicated domains, SIAM Journal on Scientific Computing, 35 (2013), A1417A1439. https://doi.org/10.1137/120877246
- J. Wang, and X. Ye, A weak Galerkin finite element method for second-order elliptic problems, Journal of Computational and Applied Mathematics, 241 (2013), 103-115. https://doi.org/10.1016/j.cam.2012.10.003
- L. Mu, J. Wang and X. Ye, Weak Galerkin finite element methods on polytopal meshes, International Journal of Numerical Analysis and Modeling, 12 (2015), 31-53.
- E. T. Chung and B. Engquist Optimal discontinuous Galerkin methods for wave propagation, SIAM Journal on Numerical Analysis, 44 (2006), 2131-2158. https://doi.org/10.1137/050641193
- E. T. Chung and B. Engquist Optimal discontinuous Galerkin methods for the acoustic wave equation in higher dimensions, SIAM Journal on Numerical Analysis, 47 (2009), 3820-3848. https://doi.org/10.1137/080729062
- E. T. Chung and W. Qiu, Analysis of an SDG method for the incompressible Navier-Stokes equations, SIAM Journal on Numerical Analysis, 55 (2017), 543-569. https://doi.org/10.1137/15M1038694
- E. T. Chung, P. Ciarlet Jr. and T. Yu, Convergence and superconvergence of staggered discontinuous Galerkin methods for the three-dimensional Maxwells equations on Cartesian grids, Journal on Computational Physics, 235 (2013), 14-31. https://doi.org/10.1016/j.jcp.2012.10.019
- E. T. Chung, H. H. Kim and O.B. Widlund, Two-level overlapping Schwarz algorithms for a staggered discontinuous Galerkin method, SIAM Journal on Numerical Analysis, 51 (2013), 47-67. https://doi.org/10.1137/110849432
- H. H. Kim, E. T. Chung and C. S. Lee, A staggered discontinuous Galerkin method for the Stokes system, SIAM Journal on Numerical Analysis, 51 (2013), 3327-3350. https://doi.org/10.1137/120896037
- E. T. Chung, C. Cockburn and G. Fu, The staggered DG method is the limit of a hybridizable DG method, SIAM Journal on Numerical Analysis, 52 (2014), 915-932. https://doi.org/10.1137/13091573X
- H. H. Kim, E. T. Chung and C.Y. Lam, Mortar formulation for a class of staggered discontinuous Galerkin methods, Computers & Mathematics with Applications, 71 (2016), 1568-1585. https://doi.org/10.1016/j.camwa.2016.02.035
- J.J. Lee and H. H. Kim, Analysis of a staggered discontinuous Galerkin method for linear elasticity, Journal of Scientific Computing, 66 (2016), 625-649. https://doi.org/10.1007/s10915-015-0036-1
- L. Zhao and E.-J. Park, Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations, Computers & Mathematics with Applications, 75 (2018), 4115-4134. https://doi.org/10.1016/j.camwa.2018.03.018
- E. T. Chung, E.-J. Park and L. Zhao, Guaranteed a posteriori error estimates for a staggered discontinuous Galerkin method, Journal of Scientific Computing, 75 (2018), 1079-1101. https://doi.org/10.1007/s10915-017-0575-8
- L. Zhao and E.-J. Park, A priori and a posteriori error analysis for a staggered discontinuous Galerkin method for convection dominant diffusion equations, Journal of Computational and Applied Mathematics, 346 (2019), 63-83. https://doi.org/10.1016/j.cam.2018.06.040
- L. Zhao and E.-J. Park, A staggered discontinuous Galerkin method of minimal dimension on quadrilateral and polygonal meshes, SIAM Journal on Scientific Computing, 40 (2018), A2543-A2567. https://doi.org/10.1137/17M1159385
- L. Zhao, E.-J. Park and D.-w. Shin, A staggered DG method of minimal dimension for the Stokes equations on general meshes, Computer Methods in Applied Mechanics and Engineering, 345 (2019), 854-875. https://doi.org/10.1016/j.cma.2018.11.016
- L. Zhao and E.-J. Park, A lowest-order staggered DG method for the coupled Stokes-Darcy problem, IMA Journal of Numerical Analysis, 40 (2020), 2871-2897. https://doi.org/10.1093/imanum/drz048
- L. Zhao, E. T. Chung and M. Lam, A new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limits, Computer Methods in Applied Mechanics and Engineering, 364 (2020), Paper No.112986, 13 pp.
- L. Zhao and E.-J. Park, A new hybrid staggered discontinuous Galerkin method on general meshes, Journal of Scientific Computing, 82 (2020), Paper No.12, 33 pp.
- L. Zhao and E.-J. Park, A staggered cell-centered DG method for linear elasticity on polygonal meshes, SIAM Journal on Scientific Computing, 42 (2020), A2158-A2181. https://doi.org/10.1137/19M1278016
- L. Zhao, E.-J. Park and E. T. Chung, Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number, Computers & Mathematics with Applications, 80 (2020), 2676-2690. https://doi.org/10.1016/j.camwa.2020.09.019
- L. Zhao, E. T. Chung, E.-J. Park, and G. Zhou, Staggered DG Method for Coupling of the Stokes and Darcy-Forchheimer Problems, SIAM Journal on Numerical Analysis 59 (2021), 1-31. https://doi.org/10.1137/19M1268525
- L. Zhao, D. Kim, E.-J. Park and E. Chung, Staggered DG method with small edges for Darcy flows in fractured porous media, https://arxiv.org/abs/2005.10955.
- D. Kim, L. Zhao and E.-J. Park, Staggered DG methods for the pseudostress-velocity formulation of the Stokes equations on general meshes, SIAM Journal on Scientific Computing, 42 (2020), A2537-A2560. https://doi.org/10.1137/20M1322170
- Y. Jeon, E.-J. Park, A hybrid discontinuous Galerkin method for elliptic problems, SIAM J. Numer. Anal. 48 (5) (2010) 1968-1983. https://doi.org/10.1137/090755102
- Y. Jeon, E.-J. Park, New locally conservative finite element methods on a rectangular mesh, Numerische Mathematik, 123 (2013), no.1, 97-119. https://doi.org/10.1007/s00211-012-0477-5
- Y. Jeon, E.-J. Park, D. Sheen, A hybridized finite element method for the Stokes problem, Computers & Mathematics with Applications Vol. 68, No. 12 Part B, (2014), 2222-2232. https://doi.org/10.1016/j.camwa.2014.08.005
- Y. Jeon, and E.-J. Park, D.-w. Shin, Hybrid Spectral Difference Methods for an Elliptic Equation, Comput. Methods Appl. Math. vol.17 no.2 (2017), 253-267. https://doi.org/10.1515/cmam-2016-0043
- S. Yadav, A. Pani, and E.-J. Park, Superconvergent discontinuous Galerkin methods for nonlinear elliptic equations, Math. Comp. 82 (2013), no. 283, 1297-1335. https://doi.org/10.1090/S0025-5718-2013-02662-2
- M.-Y. KIM AND M. F. WHEELER, A multiscale discontinuous galerkin method for convection-diffusion-reaction problems, Computers & Mathematics with Applications, 68 (2014), pp. 2251-2261. https://doi.org/10.1016/j.camwa.2014.08.007
- T. Arbogast, C. N. Dawson, P. T. Keenan, M. F. Wheeler, and I. Yotov, Enhanced cell-centered finite differences for elliptic equations on general geometry, SIAM Journal on Scientific Computing, 19 (1998), 404-425. https://doi.org/10.1137/S1064827594264545