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