تقرير
Weak discrete maximum principle and $L^\infty$ analysis of the DG method for the Poisson equation on a polygonal domain
| العنوان: | Weak discrete maximum principle and $L^\infty$ analysis of the DG method for the Poisson equation on a polygonal domain |
|---|---|
| المؤلفون: | Chiba, Yuki, Saito, Norikazu |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65N15, 65N30 |
| الوصف: | We derive several $L^\infty$ error estimates for the symmetric interior penalty (SIP) discontinuous Galerkin (DG) 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 $L^\infty$ estimates using this WMP and several $W^{2,p}$ and $W^{1,1}$ estimates for the Poisson equation. Numerical examples to validate our results are also presented. Comment: 18 pages, 4 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s13160-019-00365-3 |
| URL الوصول: | http://arxiv.org/abs/1812.00610 |
| رقم الأكسشن: | edsarx.1812.00610 |
| قاعدة البيانات: | arXiv |
كن أول من يترك تعليقا!