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Erratum to the paper 'L∞(L∞)-boundedness and convergence of DG(p)-solutions for nonlinear conservation laws with boundary conditions'
- Source :
- IMA Journal of Numerical Analysis. 35:1483-1485
- Publication Year :
- 2015
- Publisher :
- Oxford University Press (OUP), 2015.
-
Abstract
- In the paper (HA14), unfortunately, a computational error occurred in one estimate. Although the wrong estimate does not affect the main results, we want to present the necessary corrections. Essentially, Lemma 5.2 has to be corrected and, since it is used in the proof of Theorem 5.1, the proof of this theorem also requires an adaptation. (i) The corrected formulation of Lemma 5.2 is as follows. Lemma 5.2 For Lagrange finite elements with a shape-regular family of affine meshes { T n h } h>0 there is a constant C > 0 independent of q and h such that for all w ∈ Wh and q = 2m, m ∈N: CΛq−2 p (∇w,∇Ip h (wq−1))T ∫ T ‖∇w‖l2‖w‖ q−2 0,∞,T dx, ∀T ∈ T n h , (5.1) where Λp = ‖ ∑ndof i=1 |φi|‖0,∞,T is the Lebesgue constant.
- Subjects :
- Conservation law
Pure mathematics
Lemma (mathematics)
Applied Mathematics
General Mathematics
Mathematical analysis
Lebesgue integration
Computational Mathematics
Nonlinear system
symbols.namesake
Convergence (routing)
symbols
Boundary value problem
Affine transformation
Constant (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 14643642 and 02724979
- Volume :
- 35
- Database :
- OpenAIRE
- Journal :
- IMA Journal of Numerical Analysis
- Accession number :
- edsair.doi...........4a7498c0156c22177e0fabc6e114bf17