A Two-Point Boundary Value Problem by Using a Mixed Finite Element Method

DOI: 10.4236/am.2015.612177   PDF   HTML   XML   2,510 Downloads   2,965 Views   Citations


This paper describes a numerical solution for a two-point boundary value problem. It includes an algorithm for discretization by mixed finite element method. The discrete scheme allows the utilization a finite element method based on piecewise linear approximating functions and we also use the barycentric quadrature rule to compute the stiffness matrix and the L2-norm.

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Alzate, P. and Granada, J. (2015) A Two-Point Boundary Value Problem by Using a Mixed Finite Element Method. Applied Mathematics, 6, 1996-2003. doi: 10.4236/am.2015.612177.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Brezzi, F. (1974) On the Existence, Uniqueness and Approximation of Saddle Points Problems Arising from Lagrangian Multipliers. ESAIM: Mathematical Modelling and Numerical Analysis—Modélisation Mathématique et Analyse Numérique, 8, 129-151.
[2] Larsson, S. and Thome, V. (2009) Partial Differential Equations with Numerical Methods. Springer-Verlag, New York.
[3] Canuto, C. and Hussaini, M. (1988) Spectral Methods in Fluids Dynamics. Springer Series in Computational Physics, Springer-Verlag, Berlin.
[4] Fortin, M. (1977) An Analysis of the Convergence of Mixed Finite Element Methods. R.A.I.R.O, 11, 341-354.
[5] Guzman, J. (2010) A Unified Analysis of Several Mixed Methods for Elasticity with Weak Stress Symmetric. Journal of Scientific Computing, 4, 156-169.
[6] Yao, C. and Jia, S. (2014) Asymptotic Expansion Analysis of Nonconforming Mixed Finite Element Methods for Time-Dependent Maxwell’s Equations in Debye Medium. Applied Mathematics and Computation, 229, 34-40.
[7] Pal, M. and Lamine, S. (2015) Validation of the Multiscale Mixed Finite-Element Method. International Journal for Numerical Methods in Fluids, 77, 206-223.

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