Lectures in course MATH-451: Numerical approximation of PDEs

Explores well-posedness and comparison principles for elliptic equations and their implications.

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

Covers the application of finite difference methods to solve partial differential equations.

Explores numerical computing stability, error analysis, and truncation error impact.

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Explores numerical methods for solving partial differential equations computationally, emphasizing their importance in predicting various phenomena.

Explores weak formulations and solutions for elliptic problems using Galerkin methods.

Explores linear partial differential equations, elliptic PDEs, Laplace equation, boundary conditions, and classical solutions.

Explores stability, consistency, and convergence in numerical methods, emphasizing the importance of order consistency and boundary conditions.

Covers the evaluation of projects, project slots, heat integration, weak solutions, and projection of solutions.

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

Covers the renumbering of stencil points and the impact of boundary corrections on the linear system matrix.

Covers band matrices, linear systems, stability analysis, and boundary corrections in numerical methods.

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

Covers error estimation in numerical methods, focusing on stability and truncation errors.

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

Covers the Galerkin method in the Finite Element Method for solving non-homogeneous Dirichlet problems.

Covers weak solutions in the finite element method, emphasizing continuity and the Cauchy-Schwarz inequality.

Explains Galerkin orthogonality in numerical methods and its stability criteria.

Covers the assembly of finite element matrix and diffusion coefficients.