**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32731

##### A Finite Point Method Based on Directional Derivatives for Diffusion Equation

**Authors:**
Guixia Lv,
Longjun Shen

**Abstract:**

**Keywords:**
Finite point method,
directional derivatives,
diffusionequation,
method for selecting neighbor point set.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1334291

**References:**

[1] L. J. Shen, G. X. Lv and Z. J. Shen, "A Finite Point Method Based on Directional Differences", SIAM J. Numer. Anal., vol. 47(3), pp. 2224- 2242, 2009.

[2] G. X. Lv, L. J. Shen and Z. J. Shen, "Study on Finite Point Method", Chinese J. comput. phys., vol. 25(5), pp. 505-524, 2008.

[3] E. O╦£nate, S. Idelsohn, O. C. Zienkiewicz, and R. L. Taylor, "A finite point method in computing mechanics application to convective transport and fluid flow", Internat. J. Numer. Methods Engrg., vol. 39, pp. 3839-3866, 1996.

[4] B. Boroomand, A. A. Tabatabaei, and E. O╦£nate, "Simple modifications for stabilization of the finite point method", Intern. J. Numer. Methods Engrg., vol. 63, pp. 351-379, 2005.

[5] Z. J. Shen, L. J. Shen, G. X. Lv,W. Chen, and G. W. Yuan, "A Lagrangian finite point method for two-dimensional fluid dynamic problems", Chinese J. comput. phys., vol. 22(5), pp. 377-385, 2005.

[6] D. Sridar and N. Balakrishnan, "An upwind finite difference scheme for meshless solvers", J. Comput. Phys., vol. 189, pp. 1-29, 2003.

[7] P. S. Jensen, "Finite difference techniques for variable grids", Comp. Structures, vol. 2, pp. 17-29, 1972.

[8] K. C. Chung, "A generalized finite difference method for heat transfer problems of irregular geometries", Numer. Heat Transfer, Part A: Applications, vol. 4, pp. 345-357, 1981.

[9] G. B. Wright and B. Fornberg, "Scattered node compact finite differencetype formulas generated from radial basis functions", J. Comput. Phys., vol. 212, pp. 99-123, 2006.

[10] J. M. Wu, Z. H. Dai, Z. M. Gao and G. W. Yuan, "The linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes", J. Comput. Phys., vol. 229, pp. 3382-3401, 2010.