Numerical solution of semi-linear advection-diffusion-reaction equations by discontinuous Galerkin methods

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Thesis Type: Postgraduate

Institution Of The Thesis: Orta Doğu Teknik Üniversitesi, Institute of Applied Mathematics, Turkey

Approval Date: 2016

Student: SÜLEYMAN YILDIZ

Supervisor: BÜLENT KARASÖZEN

Abstract:

IIn this thesis, we study splitting methods for semi-linear advection-diffusion-reaction (ADR) equations which are discretized by the symmetric interior penalty Galerkin (SIPG) method in space. For the time integration Rosenbrock methods are used with Strang splitting. The linear system of equations are solved iteratively by preconditioned generalized minimum residual method (GMRES). Numerical experiments for ADR equations with different type nonlinearities demonstrate the effectiveness of the proposed approach.