Finite Element Discretization: Heat Equation

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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.