MATH-451: Numerical approximation of PDEs

Lectures in this course (52)

Explores Poincare inequality, continuity, and weak formulations in solving differential equations.

Covers finite element spaces, conforming mesh construction, Galerkin error analysis, and best approximation error.

Explains the construction of basis functions in the Finite Element Method, focusing on local to global mapping and numerical accuracy.

Explores inverse inequality and stability conditions in numerical methods.

Explores barycentric coordinates, interpolation, and basis functions in the context of linear systems.

Discusses interpolation points and mixed boundary conditions in numerical analysis, emphasizing convergence properties and stability implications.

Explores energy conservation in wave equations, emphasizing uniqueness, existence of solutions, and stability.

Discusses mapping local to global coordinates in finite element analysis and the importance of vertex numbering.

Explores norm equivalence, inverse inequality, and error analysis in finite element methods.

Explores finite element discretization of the heat equation and its verification process.

Explores best approximation error and Shiffnen matrix properties in linear algebra.

Covers the assembly process of the finite element matrix and strategies to solve system conditions.

Explores the basics of the heat equation, focusing on diffusion and stability estimates.

Covers interpolation in finite element spaces and the regularity of solutions in convex domains.

Explores consistency and stability in numerical methods, emphasizing error analysis and the role of boundary conditions.

Explores the Poincaré - Friedrichs theorem and kernel inequality in constant conditions and boundary uniqueness.

Covers the error analysis of a discrete finite difference scheme, focusing on stability and perturbation.

Covers the error analysis for the Galerkin scheme and the importance of Galerkin orthogonality.

Covers the convection diffusion equation and its numerical approximation methods.

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

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