MATH-451: Numerical approximation of PDEs

Lectures in this course (52)

Explores streamline diffusion and emphasizes fully consistent numerical methods.

Covers the process of estimating stability and quality in numerical methods, focusing on discrete problems and algebraic identities.

Covers mathematical estimations and algebraic identities in fully discrete problems.

Explores the Newmark scheme's energy conservation principles in explicit and implicit formulations.

Covers the continuous problem of the wave equation and its migration.

Explores the conservation of energy in the Newmark scheme and its implications for stability and error estimates.

Covers the application of Newmark schemes for time discretization in the context of energy conservation.

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

Covers linear PDEs of order 2, focusing on elliptic second-order PDEs and boundary conditions.

Explores the maximum principle in elliptic problems and its implications, including inverse monotonicity and comparison functions.

Explains stiffness matrix in FEM and the role of basis functions.

Explores weak formulations, Galerkin method, and variational formulations in finite element methods.

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