Please use this identifier to cite or link to this item:
Title: Pointwise Error Estimates and Two-Grid Algorithms of Discontinuous Galerkin Method for Strongly Nonlinear Elliptic Problems
Authors: Bi, C
Wang, C
Lin, Y 
Keywords: Discontinuous Galerkin methods
Nonlinear problems
Pointwise error estimates
Two-grid algorithms
Issue Date: 2015
Publisher: Springer
Source: Journal of scientific computing, 2015 How to cite?
Journal: Journal of scientific computing 
Abstract: In this paper, we consider the discontinuous Galerkin finite element method for the strongly nonlinear elliptic boundary value problems in a convex polygonal (Formula presented.) Optimal and suboptimal order pointwise error estimates in the (Formula presented.)-seminorm and in the (Formula presented.)-norm are established on a shape-regular grid under the regularity assumptions (Formula presented.). Moreover, we propose some two-grid algorithms for the discontinuous Galerkin method which can be thought of as some type of linearization of the nonlinear system using a solution from a coarse finite element space. With this technique, solving a nonlinear elliptic problem on the fine finite element space is reduced into solving a linear problem on the fine finite element space and solving the nonlinear elliptic problem on a coarser space. Convergence estimates in a mesh-dependent energy norm are derived to justify the efficiency of the proposed two-grid algorithms. Numerical experiments are also provided to confirm our theoretical findings.
ISSN: 0885-7474
DOI: 10.1007/s10915-015-0072-x
Appears in Collections:Journal/Magazine Article

View full-text via PolyU eLinks SFX Query
Show full item record

Page view(s)

Last Week
Last month
Checked on Aug 20, 2017

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.