On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes

Abdellatif Agouzal, Konstantin Lipnikov and Yuri V. Vassilevski

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 10, 1949-1961

Abstract: We describe a new method for generating meshes that minimize the gradient of a discretization error. The key element of this method is construction of a tensor metric from edge-based error estimates. In our papers [1–4] we applied this metric for generating meshes that minimize the gradient of P1-interpolation error and proved that for a mesh with N triangles, the L2-norm of gradient of the interpolation error is proportional to N−1/2. In the present paper we recover the tensor metric using hierarchical a posteriori error estimates. Optimal reduction of the discretization error on a sequence of adaptive meshes will be illustrated numerically for boundary value problems ranging from a linear isotropic diffusion equation to a nonlinear transonic potential equation.

Keywords: Metric-based adaptation; Finite element method; Quasi-optimal meshes (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475410004283
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:10:p:1949-1961

DOI: 10.1016/j.matcom.2010.12.027

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().