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Volume 3, Issue 4
An H¹-Galerkin Mixed Finite Element Method for the Extended Fisher-Kolmogorov Equation

L. JONES TARCIUS DOSS AND A. P. NANDINI

Int. J. Numer. Anal. Mod. B, 3 (2012), pp. 460-485

Published online: 2012-03

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  • Abstract
An H^1-Galerkin mixed finite element method is applied to the extended Fisher-Kolmogorov equation by employing a splitting technique. The method described in this paper may also be considered as a Petrov-Galerkin method with cubic spline space as trial space and piecewise linear space as test space, since second derivative of a cubic spline is a linear spline. Optimal order error estimates are obtained without any restriction on the mesh. Fully discrete scheme is also discussed and optimal order estimates are obtained. The results are validated with numerical examples.
  • Keywords

Extended FisherKolmogorov (EFK) equation Second-order splitting H^1-Galerkin method Auxiliary projection Semi and Fully discrete schemes A priori bounds Optimal order error estimates Cubic B-splines

  • AMS Subject Headings

65N30 65N15 65M60 65M15 35G20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-3-460, author = {L. JONES TARCIUS DOSS AND A. P. NANDINI}, title = {An H¹-Galerkin Mixed Finite Element Method for the Extended Fisher-Kolmogorov Equation}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2012}, volume = {3}, number = {4}, pages = {460--485}, abstract = {An H^1-Galerkin mixed finite element method is applied to the extended Fisher-Kolmogorov equation by employing a splitting technique. The method described in this paper may also be considered as a Petrov-Galerkin method with cubic spline space as trial space and piecewise linear space as test space, since second derivative of a cubic spline is a linear spline. Optimal order error estimates are obtained without any restriction on the mesh. Fully discrete scheme is also discussed and optimal order estimates are obtained. The results are validated with numerical examples.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/295.html} }
TY - JOUR T1 - An H¹-Galerkin Mixed Finite Element Method for the Extended Fisher-Kolmogorov Equation AU - L. JONES TARCIUS DOSS AND A. P. NANDINI JO - International Journal of Numerical Analysis Modeling Series B VL - 4 SP - 460 EP - 485 PY - 2012 DA - 2012/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/295.html KW - Extended FisherKolmogorov (EFK) equation KW - Second-order splitting KW - H^1-Galerkin method KW - Auxiliary projection KW - Semi and Fully discrete schemes KW - A priori bounds KW - Optimal order error estimates KW - Cubic B-splines AB - An H^1-Galerkin mixed finite element method is applied to the extended Fisher-Kolmogorov equation by employing a splitting technique. The method described in this paper may also be considered as a Petrov-Galerkin method with cubic spline space as trial space and piecewise linear space as test space, since second derivative of a cubic spline is a linear spline. Optimal order error estimates are obtained without any restriction on the mesh. Fully discrete scheme is also discussed and optimal order estimates are obtained. The results are validated with numerical examples.
L. JONES TARCIUS DOSS AND A. P. NANDINI. (2012). An H¹-Galerkin Mixed Finite Element Method for the Extended Fisher-Kolmogorov Equation. International Journal of Numerical Analysis Modeling Series B. 3 (4). 460-485. doi:
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