Adaptive discontinuous galerkin methods for non-linear reactive flows

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2014

Author

Uzunca, Murat

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The aim of this thesis is to solve the convection/reaction dominated non-stationary semi-linear diffusion-convection-reaction problems with internal/boundary layers in an accurate and efficient way using a time-space adaptive algorithm. We use for space discretization the symmetric interior penalty discontinuous Galerkin method, and backward Euler for time discretization. Our main interest is to derive robust residual-based a posteriori error estimators both in space and time. To derive the a posteriori bounds for the fully discrete system, we utilize the elliptic reconstruction technique. The use of elliptic reconstruction technique allows us to use the a posteriori error estimators derived for stationary models and to obtain optimal orders in $L^{\infty}(L^2)$ norms.

Subject Keywords

Galerkin methods., Numerical analysis., Finite element method.

URI

http://etd.lib.metu.edu.tr/upload/12618224/index.pdf
https://hdl.handle.net/11511/24236

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

M. Uzunca, “Adaptive discontinuous galerkin methods for non-linear reactive flows,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.