A high order composite scheme for the second order elliptic problem with nonlocal boundary and its fast algorithm

The elliptic problem with nonlocal boundary condition is widely applied in the field of science and engineering. Firstly, we construct a linear finite element scheme for the nonlocal boundary problem, and derive the optimal L2 error estimate. Then, based on the quadratic finite element and the extra...

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Vydané v:	Applied mathematics and computation Ročník 227; s. 212 - 221
Hlavní autori:	Nie, Cunyun, Shu, Shi, Yu, Haiyuan, An, Qianjiang
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 15.01.2014
Predmet:	Algebraic multigrid method Algorithms An upper triangular preconditioner Boundaries Design engineering Discrete systems Extrapolation Finite element method Mathematical analysis Optimization The elliptic problem with nonlocal boundary condition The finite element method The elliptic problem with nonlocal boundary condition An upper triangular preconditioner Algebraic multigrid method The finite element method
ISSN:	0096-3003, 1873-5649
On-line prístup:	Získať plný text
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Popis
Shrnutí:	The elliptic problem with nonlocal boundary condition is widely applied in the field of science and engineering. Firstly, we construct a linear finite element scheme for the nonlocal boundary problem, and derive the optimal L2 error estimate. Then, based on the quadratic finite element and the extrapolation linear finite element methods, we present a composite scheme, and prove that it is convergent order three. Furthermore, we design an upper triangular preconditioning algorithm for the linear finite element discrete system. Finally, numerical results not only validate that the new algorithm is efficient, but also show that the new scheme is convergent order three, furthermore order four on uniform grids.
Bibliografia:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0096-3003 1873-5649
DOI:	10.1016/j.amc.2013.10.066