Lectures related to Finite Element Method: Key Concepts

Power Systems Dynamics: Transient Stability

Explores transient stability in power systems dynamics, covering algebraic equations, generator models, and numerical integration techniques.

Numerical Differentiation and Integration

Explores numerical differentiation and integration methods, emphasizing the accuracy of finite differences in computing derivatives and integrals.

Numerical Differentiation and Integration

Covers numerical differentiation and integration techniques using examples and quadrature formulas.

Numerical Differentiation and Integration

Covers numerical differentiation, integration, finite differences, Taylor expansions, and interpolation polynomials.

Hydroacoustic Modeling: Electrical Analogy

Explores hydroacoustic modeling through electrical analogies, discussing resolution methods, simplified equations, and physical interpretations.

Numerical Analysis: Introduction to Computational Methods

Covers the basics of numerical analysis and computational methods using Python, focusing on algorithms and practical applications in mathematics.

Explicit Stabilised Methods: Stochastic Differential Equations

Covers explicit stabilized methods for stiff stochastic differential equations, analyzing their properties and applications.

Molecular dynamics under constraints

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Ordinary Differential Equations: Non-linear Analysis

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Numerical Methods for Boundary Value Problems

Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.

Numerical Integration: Trapezoidal Rule

Covers numerical integration methods, focusing on the trapezoidal rule and iterative processes.

Computational Geomechanics: Poroelasticity and Transient Flow

Explores poroelasticity, porosity variation, weak form derivation, and numerical integration in transient flow problems.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Variational Formulation: Finite Element Method

Discusses the variational formulation of the heat equation using the finite element method.

Nonlinear Analysis of Structures: Integration Methods

Covers integration methods and element stiffness matrices for nonlinear structural analysis.

Nonlinear Geometric Transformation: Analysis and Approximations

Explores nonlinear geometric transformations in structural engineering, emphasizing accurate integration methods and practical applications.

Error Estimation in Numerical Methods

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Finite element methods

Covers finite element methods for solving diffusion problems in porous media, including meshing, interpolation, and weighted residuals.

Interpolatory Quadrature Formulas

Covers interpolatory quadrature formulas for approximating definite integrals using polynomials and discusses the uniqueness of solutions and practical applications in numerical integration.