Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/29090
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.
URI: http://hdl.handle.net/10397/29090
ISSN: 0885-7474
DOI: 10.1007/s10915-015-0072-x
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