ON THE CONVERGENCE OF THE DISCONTINUOUS GALERKIN SCHEME FOR EINSTEIN-SCALAR EQUATIONS

被引：0

作者：

Chen, Yuewen ^{[1
]}

Shu, Chi-wang ^{[2
]}

Yau, Shing-tung ^{[1
,3
]}

机构：

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[3] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China

来源：

MATHEMATICS OF COMPUTATION | 2025年

关键词：

Einstein-scalar equations; discontinuous Galerkin scheme; FINITE-ELEMENT-METHOD; CONSERVATION-LAWS; GENERALIZED SOLUTIONS; NUMERICAL RELATIVITY; GRAVITATIONAL-WAVES; BOUNDARY-CONDITIONS; SMOOTH SOLUTIONS; EVOLUTION;

D O I：

10.1090/mcom/4077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the stability and convergence of the high order discontinuous Galerkin scheme to spherically symmetric Einstein-scalar equations for a class of large initial data that ensures the formation of a black hole. Having chosen the Bondi coordinate system, we achieve L2 stability and obtain the optimal error estimates.

引用

页数：31

共 50 条

[41] A robust discontinuous Galerkin scheme on anisotropic meshes
Kashiwabara, Takahito
Tsuchiya, Takuya
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2021, 38 (03) : 1001 - 1022
[42] Central discontinuous Galerkin methods on overlapping meshes for wave equations
Liu, Yong
Lu, Jianfang
Shu, Chi-Wang
Zhang, Mengping
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2021, 55 (01) : 329 - 356
[43] SUPERCONVERGENCE OF DISCONTINUOUS GALERKIN AND LOCAL DISCONTINUOUS GALERKIN SCHEMES FOR LINEAR HYPERBOLIC AND CONVECTION-DIFFUSION EQUATIONS IN ONE SPACE DIMENSION
Cheng, Yingda
Shu, Chi-Wang
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 47 (06) : 4044 - 4072
[44] CONVERGENCE OF DISCONTINUOUS GALERKIN SCHEMES FOR FRONT PROPAGATION WITH OBSTACLES
Bokanowski, Olivier
Cheng, Yingda
Shu, Chi-Wang
MATHEMATICS OF COMPUTATION, 2016, 85 (301) : 2131 - 2159
[45] Stabilized discontinuous Galerkin method for hyperbolic equations
Calle, JLD
Devloo, PRB
Gomes, SM
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2005, 194 (17) : 1861 - 1874
[46] An embedded discontinuous Galerkin method for the Oseen equations
Han, Yongbin
Hou, Yanren
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS, 2021, 55 (05) : 2349 - 2364
[47] The spherically symmetric Einstein-scalar field system with positive and vanishing cosmological constant: a comparison
Costa, Joao L.
GENERAL RELATIVITY AND GRAVITATION, 2013, 45 (12) : 2415 - 2440
[48] A positivity-preserving high order discontinuous Galerkin scheme for convection-diffusion equations
Srinivasan, Sashank
Poggie, Jonathan
Zhang, Xiangxiong
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 366 : 120 - 143
[49] Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms
Huang, Juntao
Shu, Chi-Wang
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 361 : 111 - 135
[50] Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem
Adjerid, Slimane
Massey, Thomas C.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 195 (25-28) : 3331 - 3346

← 1 2 3 4 5 →