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Development and application of an adaptive finite element method to reaction‐diffusion equations
Author(s) -
Ramos J. I.
Publication year - 1985
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650050103
Subject(s) - finite element method , smoothed finite element method , mathematics , galerkin method , mixed finite element method , extended finite element method , laminar flow , adaptive mesh refinement , finite difference , hp fem , finite difference method , collocation (remote sensing) , finite element limit analysis , boundary knot method , finite difference coefficient , discontinuous galerkin method , mathematical analysis , mechanics , computer science , boundary element method , physics , engineering , structural engineering , computational science , machine learning
An adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed‐node finite‐difference schemes and an adaptive finite‐difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth‐order accurate, fixed‐node, finite‐difference methods when 272 collocation points are employed in the calculations.