A Splitting Extrapolation for Solving Nonlinear Elliptic Equations with D-quadratic Finite Elements

Editor(s)

Tryggvason, G.

Abstract

Nonlinear elliptic partial differential equations are important to many large scale engineering and science problems. For this kind of equations, this article discusses a splitting extrapolation which possesses a high order of accuracy, a high degree of parallelism, less computational complexity and more flexibility than Richardson extrapolation. According to the problems, some domain decompositions are constructed and some independent mesh parameters are designed. Multi-parameter asymptotic expansions are proved for the errors of approximations. Based on the expansions, splitting extrapolation formulas are developed to compute approximations with high order of accuracy on a globally fine grid. Because these formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid, a large scale multidimensional problem is turned into a set of smaller discrete subproblems. Additionally, this method is efficient for solving interface problems.

Department(s)

Mathematics and Statistics

Keywords and Phrases

extrapolation; asymptotic expansion; parallel algorithm; finite elements; Domain decomposition; A posteriori error estimate

International Standard Serial Number (ISSN)

0021-9991

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2009 Elsevier, All rights reserved.

Publication Date

01 Jan 2009

Link to Full Text

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