In these two hours we will give a brief introduction to high order accurate finite difference, discontinuous Galerkin finite element, and spectral methods for solving partial differential equations arising from astrophysics. The following topics will be addressed:
-- hyperbolic conservation laws, structures of their solutions (shocks, contacts, ...)
-- conservative finite difference methods, high order accuracy, WENO (weighted essentially non-oscillatory) scheme as an example
-- discontinuous Galerkin finite element method for conservation laws, basic algorithm structure, properties of the algorithm,comparison with finite difference methods
-- spectral method, Galerkin versus collocation, filters, spectral vanishing viscosity
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