Numerical Analysis: Solving Linear Systems in Higher Dimensions

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Finite Differences and Finite Elements: Variational Formulation

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

Numerical Methods for Boundary Value Problems

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

Iterative Methods: Jacobi

Covers the Jacobi iterative method for solving electrostatic problems and discusses convergence and practical examples.

Computational Geomechanics: Week 4

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Numerical Methods: Boundary Value Problems

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

Finite Elements: Problem with Limits

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

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Diffusion-Convection: Modeling and Schemes

Covers modeling and numerical schemes for diffusion-convection problems.

Boundary Value Problems: Numerical Methods

Covers the motivation and examples of boundary value problems, the finite difference method, and the approximation of local derivatives.

Linear Statics of Deformable Solids

Introduces linear statics for linear elastic solids in small deformations, stress equilibrium, the Virtual Work Principle, and the Finite Element Method.