A Splitting Extrapolation for Solving Nonlinear Elliptic Equations with D-quadratic Finite ElementsJournal of Computational Physics
AbstractNonlinear 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
- asymptotic expansion,
- parallel algorithm,
- finite elements,
- Domain decomposition,
- A posteriori error estimate
Document TypeArticle - Journal
Rights© 2009 Elsevier, All rights reserved.
Citation InformationYong Cao, Xiaoming He and Tao Lü. "A Splitting Extrapolation for Solving Nonlinear Elliptic Equations with D-quadratic Finite Elements" Journal of Computational Physics (2009)
Available at: http://works.bepress.com/xiaoming-he/17/