Lectures related to Finite Elements: Elasticity and Variational Formulation

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Finite Elements: Problem with Limits

Covers the application of finite element methods to solve boundary value problems in one dimension.

Elasticity: Constitutive Modelling in Geomechanics

Explores constitutive equations in geomechanics, stress-strain behavior, and practical applications in engineering.

Finite Element Analysis: Advanced Mechanisms in Engineering

Provides an overview of advanced mechanisms analysis using Finite Element Method and Finite Element Analysis in engineering applications.

Elasticity: Constitutive Modelling in Geomechanics

Explores constitutive modelling in geomechanics, focusing on stress-strain behavior and the application of elastic models in analytical and numerical methods.

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Numerical Analysis: Advanced Topics

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Numerical Methods: Euler and Crank-Nicolson

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

Euler-Lagrange Equation: Convexity and Saddle Point Problems

Explores the Euler-Lagrange equation, convexity, and saddle point problems in variational calculus.

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Numerical Methods for Boundary Value Problems

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

Direct Methods for Linear Systems of Equations

Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Numerical Methods: Euler Schemes

Focuses on Euler schemes for numerical approximation of forces and velocities.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Wave Equations: Vibrating String

Explores the wave equation for a vibrating string and its numerical solution using finite difference formulas and the Newmark scheme in MATLAB/GNU Octave.

Finite Difference Methods: Stability Analysis

Explores the stability analysis of finite difference methods for solving differential equations.

Finite Elements: Crash Course on Elliptic Problems

Provides a crash course on finite elements for elliptic problems, emphasizing the Galerkin method and quasi-optimality.

Numerical Methods: Boundary Value Problems

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