Which meshes are better conditioned: adaptive, uniform, locally refined or locally adjusted?

Authors:
Sanjay Kumar Khattri;Gunnar Fladmark
Affiliations:
Department of Mathematics, University of Bergen, Norway;Department of Mathematics, University of Bergen, Norway
Venue:
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Year:
2006

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Abstract

Adaptive, locally refined and locally adjusted meshes are preferred over uniform meshes for capturing singular or localised solutions. Roughly speaking, for a given degree of freedom a solution associated with adaptive, locally refined and locally adjusted meshes is more accurate than the solution given by uniform meshes. In this work, we answer the question which meshes are better conditioned. We found, for approximately same degree of freedom (same size of matrix), it is easier to solve a system of equations associated with an adaptive mesh.