Premium
A goal‐oriented hp ‐adaptive finite element method with electromagnetic applications. Part I: electrostatics
Author(s) -
Pardo D.,
Demkowicz L.,
TorresVerdín C.,
Tabarovsky L.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1488
Subject(s) - finite element method , casing , computer science , norm (philosophy) , sequence (biology) , mathematical optimization , algorithm , mechanical engineering , mathematics , engineering , structural engineering , biology , political science , law , genetics
We describe the development and application of a finite element (FE) self‐adaptive hp goal‐oriented algorithm for elliptic problems. The algorithm delivers (without any user interaction) a sequence of optimal hp ‐grids. This sequence of grids minimizes the error of a prescribed quantity of interest with respect to the problem size. The refinement strategy is an extension of a fully automatic, energy‐norm based, hp ‐adaptive algorithm. We illustrate the efficiency of the method with 2D numerical results. Among other problems, we apply the goal‐oriented hp ‐adaptive strategy to simulate direct current (DC) resistivity logging instruments (including through casing resistivity tools) in a borehole environment and for the assessment of rock formation properties. Copyright © 2005 John Wiley & Sons, Ltd.