Lectures related to Finite Element Discretization: Heat Equation

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Maximum Principle in Heat Equation

Explores the maximum principle in the context of the heat equation and the concept of the cylinder.

Heat Equation: Separation of Variables

Covers the application of separation of variables method to solve the heat equation.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Optimal Transport: In-Depth Evaluation

Explores optimal transport theory with a focus on heat equations and Wasserstein distance.

Thermal FEM: Steady State and Transient Analysis

Explores steady-state and transient thermal analysis of silicon beams, including convection effects and practical exercises.

Heat Equation in 1D: Chapter 12

Explores the heat equation in 1D, emphasizing conservation of thermal energy and numerical solution methods.

Fourier Analysis and PDEs

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Optimal Transport: Gradient Flows

Explores optimal transport, gradient flows, the implicit Euler scheme, and the heat equation in the context of Dirichlet energy functional.

Finite Difference Methods: Heat Equation Discretization

Explains finite difference methods for heat equation discretization, emphasizing stability and precision in numerical solutions.

Introduction to Numerical Methods for PDEs

Covers the numerical approximation of PDEs and examples of nonlinear behavior.

Diffusion Equation

Covers the Fourier law, heat equation, Righi-Leduc effect, and related experiments.

Numerical Approximation of PDEs

Covers the numerical approximation of PDEs, including Poisson and heat equations, transport phenomena, and incompressible limits.

Variational Formulation: Finite Element Method

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

Heat Equation: Stationary Distribution

Explores the heat equation, equilibrium equations, heat flux, and harmonic functions in heat distribution.

Numerical Methods for Boundary Value Problems

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

Free Propagation and Heat Equation

Covers free propagation and the heat equation solution, discussing momentum preservation and Fourier multipliers.

Finite Element Method: Weak Formulation and Galerkin Method

Explores the weak formulation and Galerkin method in Finite Element Method applications, including boundary conditions and linear systems of equations.

Convolution and Fourier Transform

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.