Weak discrete maximum principle and L∞ analysis of the DG method for the Poisson equation on a polygonal domain

被引：0

作者：

Chiba, Yuki ^{[1
]}

Saito, Norikazu ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Komaba 3-8-1, Tokyo 1538914, Japan

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2019年 / 36卷 / 03期

关键词：

Discontinuous Galerkin method; Pointwise error estimate; Maximum principle; DISCONTINUOUS GALERKIN METHODS; FINITE-ELEMENT-METHOD; PENALTY;

D O I：

10.1007/s13160-019-00365-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive several L infinity error estimates for the symmetric interior penalty discontinuous Galerkin method applied to the Poisson equation in a two-dimensional polygonal domain. Both local and global estimates are examined. The weak maximum principle (WMP) for the discrete harmonic function is also established. We prove our L infinity estimates using this WMP and several W-2,W-p and W(1,1)estimates for the Poisson equation. Numerical examples to validate our results are also presented.

引用

页码：809 / 834

页数：26

共 22 条

[11] Grisvard P., 1976, NUMERICAL SOLUTION P, P207
[12] Discrete maximum principle for interior penalty discontinuous Galerkin methods
Horvath, Tamas L.
Mincsovics, Miklos E.
[J]. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2013, 11 (04): : 664 - 679
[13] Kashiwabara T., 2018, ARXIV E PRINTS
[14] Nitsche J. A., 1975, JOURNEES ELEMENTS FI, P18
[15] SOME OPTIMAL ERROR-ESTIMATES FOR PIECEWISE LINEAR FINITE-ELEMENT APPROXIMATIONS
RANNACHER, R
SCOTT, R
[J]. MATHEMATICS OF COMPUTATION, 1982, 38 (158) : 437 - 445
[16] Reed W. H, 1973, Los Alamos Report LA-UR-73-479
[17] Rivière B, 2008, FRONT APPL MATH, P3
[18] Pointwise error estimates and asymptotic error expansion inequalities for the finite element method on irregular grids: Part I. Global estimates
Schatz, AH
[J]. MATHEMATICS OF COMPUTATION, 1998, 67 (223) : 877 - 899
[19] SCHATZ AH, 1977, MATH COMPUT, V31, P414, DOI 10.1090/S0025-5718-1977-0431753-X
[20] WEAK DISCRETE MAXIMUM PRINCIPLE AND STABILITY OF THE FINITE-ELEMENT METHOD IN L-INFINITY ON PLANE POLYGONAL DOMAINS .1.
SCHATZ, AH
[J]. MATHEMATICS OF COMPUTATION, 1980, 34 (149) : 77 - 91

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