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An adaptive hp ‐version of the finite element method applied to flame propagation problems
Author(s) -
Rao V. China Venkata,
Das P. C.,
Sundararajan T.
Publication year - 1997
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/(sici)1097-0207(19970915)40:17<3181::aid-nme207>3.0.co;2-z
Subject(s) - finite element method , a priori and a posteriori , discretization , adaptive mesh refinement , degree (music) , propagation of uncertainty , dimension (graph theory) , mathematics , algorithm , mathematical optimization , computer science , mathematical analysis , philosophy , physics , computational science , epistemology , acoustics , pure mathematics , thermodynamics
Abstract This paper describes an adaptive hp ‐version mesh refinement strategy and its application to the finite element solution of one‐dimensional flame propagation problems. The aim is to control the spatial and time discretization errors below a prescribed error tolerance at all time levels. In the algorithm, the optimal time step is first determined in an adaptive manner by considering the variation of the computable error in the reaction zone. Later, the method uses a p ‐version refinement till the computable a posteriori error is brought down below the tolerance. During the p ‐version, if the maximum allowable degree of approximation is reached in some elements of the mesh without satisfying the global error tolerance criterion, then conversion from p ‐ to h ‐version is performed. In the conversion procedure, a gradient based non‐uniform h ‐version refinement has been introduced in the elements of higher degree approximation. In this way, p ‐version and h ‐version approaches are used alternately till the a posteriori error criteria are satisfied. The mesh refinement is based on the element error indicators, according to a statistical error equi‐distribution procedure. Numerical simulations have been carried out for a linear parabolic problem and premixed flame propagation in one‐space dimension. © 1997 John Wiley & Sons, Ltd.