Numerical Analysis of Partial Differential Equations (MAGIC100)
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For course description and justification, please see Syllabus and Comments.
Spring 2019 (Monday, January 21 to Friday, March 29)
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Review of relevant topics from PDEs and Analysis. Motivation and showcasing of applications from various branches of mathematics. Divided dierences. Finite dierence methods for parabolic and hyperbolic PDEs. Weak derivatives and function spaces. Variational formulation of PDEs. Galerkin projection and the construction of nite element methods for elliptic problems. Error analysis for nite element methods. Finite element methods for parabolic problems. Discontinuous Galerkin methods and basic nite volume concepts for hyperbolic PDEs. Numerical methods for nonlinear PDEs. A brief excursion to linear and nonlinear solvers. Applications.
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