Numerical Analysis of Partial Differential Equations (MAGIC100)
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Spring 2020 (Monday, January 20 to Friday, March 27)
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Review of relevant topics from PDEs and Analysis. Motivation and showcasing of applications from various branches of mathematics. Divided differences. Finite difference methods for parabolic and hyperbolic PDEs. Weak derivatives and function spaces. Variational formulation of PDEs. Galerkin projection and the construction of finite element methods for elliptic problems. Error analysis for finite element methods. Finite element methods for parabolic problems. Discontinuous Galerkin methods and basic finite volume concepts for hyperbolic PDEs. Numerical methods for nonlinear PDEs. A brief excursion to linear and nonlinear solvers. Applications.
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