May 26, 2019   9:05 a.m. Dušan
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Numerical solution and applications of the nonlinear partial differential equations

Supervisor: prof. RNDr. Karol Mikula, DrSc.

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Project description:Project deals with design of original numerical methods for solving nonlinear partial differential equations, study of their stability, convergence,, computational efficiency and parallelization, for the mathematical models describing- nonlinear thermomechanics, groundwater flow, dislocation dynamics and fluid dynamics with free boundaries modelled by evolving curves and surfaces driven by the external velocity field, anisotropy, surface and elastic energies,- filtering of 2D and 3D images and image sequences based on the nonlinear anisotropic and geometrical diffusion equations,- segmentation of 2D and 3D images using evolving geodesic and elastic curves and surfaces in Lagrangean and level-set formulations,-flow, diffusion and transport with adsorption in porous media, related contaminant transport in groundwater flow and solution of direct and inverse problems for the model parameter estimation,-geodetic boundary value problems formulated on the Earth surface as fixed or free boundary, and, their solution using finite and boundary element method.
Kind of project:APVV ()
Department:Department of Mathematics and Constructive Geometry (FCE)
Project identification:APVV-0351-07
Project status:Successfully completed
Project start date :01. 06. 2008
Project close date:30. 06. 2011
Number of workers in the project:2
Number of official workers in the project:0