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Local and parallel finite element methods based on two‐grid discretizations for unsteady convection–diffusion problem
Author(s) -
Li Qingtao,
Du Guangzhi
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22813
Subject(s) - discretization , grid , finite element method , mathematics , backward euler method , partition (number theory) , convection–diffusion equation , euler's formula , partition of unity , diffusion , regular grid , mathematical optimization , mathematical analysis , geometry , physics , combinatorics , thermodynamics
In this article, some local and parallel finite element methods are proposed and investigated for the time‐dependent convection–diffusion problem. With backward Euler scheme for the temporal discretization, the basic idea of the present methods is that for a solution to the considered equations, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure at each time step. The partition of unity is used to collect the local high frequency components to assemble a global continuous approximation. Theoretical results are obtained and numerical tests are reported to support the theoretical findings.