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A simple method to generate high‐order accurate convection operators for explicit schemes based on linear finite elements
Author(s) -
Donéa J.,
Giuliani S.
Publication year - 1981
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.1650010106
Subject(s) - simple (philosophy) , finite element method , multilinear map , mathematics , truncation error , truncation (statistics) , matrix (chemical analysis) , algorithm , calculus (dental) , pure mathematics , physics , medicine , philosophy , statistics , materials science , dentistry , epistemology , composite material , thermodynamics
Abstract A simple method is proposed to generate high‐order accurate convection operators for lumped‐explicit schemes based on linear or multilinear finite elements. The basic idea is to reduce the truncation error on the first‐order spatial derivatives by exploiting the consistent mass matrix of the finite element method in a purely explicit multistep procedure. The effectiveness of the method is demonstrated on pure convection problems in one and two dimensions.