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

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Uygulamalı Matematik Enstitüsü, Türkiye

Tezin Onay Tarihi: 2016

Öğrenci: SÜLEYMAN YILDIZ

Danışman: BÜLENT KARASÖZEN

Özet:

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.