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A Splitting Extrapolation for Solving Nonlinear Elliptic Equations with D-quadratic Finite Elements
Journal of Computational Physics
  • Yong Cao
  • Xiaoming He, Missouri University of Science and Technology
  • Tao Lü
Tryggvason, G.

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.

Mathematics and Statistics
Keywords and Phrases
  • extrapolation,
  • asymptotic expansion,
  • parallel algorithm,
  • finite elements,
  • Domain decomposition,
  • A posteriori error estimate
Document Type
Article - Journal
Document Version
File Type
© 2009 Elsevier, All rights reserved.
Publication Date
Citation Information
Yong Cao, Xiaoming He and Tao Lü. "A Splitting Extrapolation for Solving Nonlinear Elliptic Equations with D-quadratic Finite Elements" Journal of Computational Physics (2009)
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