A Mixed Finite Element Method for the Biharmonic Problem Using Biorthogonal or Quasi-Biorthogonal Systems
Date
2011
Authors
Lamichhane, Bishnu
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Springer
Abstract
We consider a finite element method based on biorthogonal or quasi-biorthogonal systems for the biharmonic problem. The method is based on the primal mixed finite element method due to Ciarlet and Raviart for the biharmonic equation. Using different finite element spaces for the stream function and vorticity, this approach leads to a formulation only based on the stream function. We prove optimal a priori estimates for both stream function and vorticity, and present numerical results to demonstrate the efficiency of the approach.
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Keywords: A-priori estimates; Biharmonic equations; Biharmonic problem; Biorthogonal; Finite element space; Mixed finite element methods; Mixed finite elements; Numerical results; Streamfunctions; Fourier analysis; Hydraulics; Nonlinear equations; Vorticity; Finite Biharmonic problem; Biorthogonal or quasi-biorthogonal system; Mixed finite elements
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Source
Journal of Scientific Computing
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Journal article
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2037-12-31