Mathematical modeling. Purpose and general principles of modeling. Benefits
mathematical modeling. Proper use of mathematical models.
Differential formulation of mathematical models. One-dimensional heat conduction problem and its mathematical formulation. Generalizing the model. The input linearity,
existence and uniqueness of solutions. Discrete input data. One-dimensional task
flexibility and other models. Multivariate models.
Variational formulation of boundary problems. Weak formulation of boundary problems and its relationship to the classical solutions. Energy and energy functional formulation.
Coercivity and boundedness. Uniqueness, continuous dependence of solutions
input data. Existence and smoothness of the solution.
Ritz - Galerkin (RG) method. RG method. Konenčných element method (FEM)
as a special case of the RG method. History MLP.
Algorithm finite element method. Assembling the stiffness matrix and vector
load. Taking into account the boundary conditions. Numerical solution of linear systems algebraic equations. Different types of finite elements.
The accuracy of finite element solutions. Priori estimate of the discretization error.
Convergence, h-and p-version FEM. Posteriori estimates. Network design for MLP
adaptive technology and optimal network.
FEM software and its use for MM. Preprocessing and postprocessing. Commercial
software systems. Solutions particularly difficult and special problems. Principles
Mathematical modeling using FEM.
mathematical modeling. Proper use of mathematical models.
Differential formulation of mathematical models. One-dimensional heat conduction problem and its mathematical formulation. Generalizing the model. The input linearity,
existence and uniqueness of solutions. Discrete input data. One-dimensional task
flexibility and other models. Multivariate models.
Variational formulation of boundary problems. Weak formulation of boundary problems and its relationship to the classical solutions. Energy and energy functional formulation.
Coercivity and boundedness. Uniqueness, continuous dependence of solutions
input data. Existence and smoothness of the solution.
Ritz - Galerkin (RG) method. RG method. Konenčných element method (FEM)
as a special case of the RG method. History MLP.
Algorithm finite element method. Assembling the stiffness matrix and vector
load. Taking into account the boundary conditions. Numerical solution of linear systems algebraic equations. Different types of finite elements.
The accuracy of finite element solutions. Priori estimate of the discretization error.
Convergence, h-and p-version FEM. Posteriori estimates. Network design for MLP
adaptive technology and optimal network.
FEM software and its use for MM. Preprocessing and postprocessing. Commercial
software systems. Solutions particularly difficult and special problems. Principles
Mathematical modeling using FEM.