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Internally discontinuous finite elements for moving interface problems
Author(s) -
Steven Grant P.
Publication year - 1982
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.1620180407
Subject(s) - quadratic equation , interface (matter) , finite element method , simple (philosophy) , grid , mathematics , poisson's equation , process (computing) , domain (mathematical analysis) , computer science , mathematical optimization , mathematical analysis , calculus (dental) , geometry , engineering , structural engineering , bubble , maximum bubble pressure method , parallel computing , medicine , philosophy , epistemology , dentistry , operating system
All physical process change with time and although physicists and engineers often freeze them to simplify their model studies, this is not always possible. Add to this the existence of several subregions within the modelling domain with different physical properties, the size and number of which change with time, and one has produced what might appear to be an intractable problem. Previous studies have shown that adaptive grids are an inconvenient way of modelling such moving interface problems and suggested that the use of a fixed grid with special discontinuous elements affords an efficient solution technique. This work presents and develops the characteristic matrices for two such elements, namely a quadratic triangle with an internal interface modelled by two straight lines and a quadratic isoparametric element. Both these elements are tested against an analytical solution to a simple Poisson equation. Such tests reveal the performance of the proposed elements to be satisfactory except for the definition of gradients near the interface.