Geodesic
Meshfree and mesh methods for system of non-linear parabolic equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 476-493

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The first aim of this work was finding an approximate solution for nonlinear free boundary-value problem which describes the mathematical model of filtration consolidation of soil using meshless method with radial basis functions (RBF). The second aim of this work was comparing numerical solutions that have been found by RBF method and finite element method (FEM). The third aim of this work was finding and comparing numerical solutions using different grids. We used an ideas of least square radial point collocation method. The proposed algorithm was tested on two-dimensoinal non-linear boundary value problem for system of three parabolic equations. Errors of difference between FEM's and RBFM's numerical solutions attained maximum in boundary points.
Keywords: nonlinear free boundary-value problem; meshless method; radial basis function; finite element method. 
@article{SEMR_2014_11_a69,
     author = {P. N. Martinyuk},
     title = {Meshfree and mesh methods for system of non-linear parabolic equations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {476--493},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a69/}
}
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P. N. Martinyuk. Meshfree and mesh methods for system of non-linear parabolic equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 476-493. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a69/