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Optimal convergence rates for the combined methods of different finite element methods
Author(s) -
Li ZiCai
Publication year - 1992
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.1690080301
Subject(s) - mathematics , finite element method , convergence (economics) , rate of convergence , mixed finite element method , mathematical optimization , extended finite element method , coupling (piping) , hp fem , boundary value problem , matrix (chemical analysis) , lagrange multiplier , boundary knot method , finite element limit analysis , mathematical analysis , boundary element method , computer science , mechanical engineering , computer network , channel (broadcasting) , physics , engineering , economics , thermodynamics , economic growth , materials science , composite material
Coupling techniques are essential to combining different numerical methods together for the purpose of solving an elliptic boundary value problem. By means of nonconforming constraints, the combinations of various Lagrange finite element methods often cause reduced rates of convergence. In this article, we present a method using penalty plus hybrid technique to match different finite element methods such that the optimal convergence rates in the ‖ · ‖ h and zero norms of errors of the solution can always be achieved. Also, such a coupling technique will lead to an optimal asymptotic condition number for the associated coefficient matrix. Moreover, this study can easily be extended for combining the finite difference method with the finite element method to also yield the optimal rate of convergence.