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- Title
A Postprocessed Flux Conserving Finite Element Solution.
- Authors
Zhang, Shangyou; Zhang, Zhimin; Zou, Qingsong
- Abstract
We propose a local postprocessing method to get a new finite element solution whose flux is conservative element-wise. First, we use the so-called polynomial preserving recovery (postprocessing) technique to obtain a higher order flux which is continuous across the element boundary. Then, we use special bubble functions, which have a nonzero flux only on one face-edge or face-triangle of each element, to correct the finite element solution element by element, guided by the above super-convergent flux and the element mass. The new finite element solution preserves mass element-wise and retains the quasioptimality in approximation. The method produces a conservative flux, of high-order accuracy, satisfying the constitutive law. Numerical tests in 2D and 3D are presented.
- Subjects
FINITE element method; POLYNOMIALS; STOCHASTIC convergence; ACCURACY; APPROXIMATION theory
- Publication
Numerical Methods for Partial Differential Equations, 2017, Vol 33, Issue 6, p1859
- ISSN
0749-159X
- Publication type
Article
- DOI
10.1002/num.22163