S. Tomov

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To my wife, Sissie, for her love, support, and encouragement throughout this seemingly never-ending task. To my parents, Wajid and Edelgard, who got me started on this path. To my boys, Alexander and Nicholas, who bring joy to my life. iii Acknowledgements * I would like to thank my adviser, Dr. Jack Dongarra for his guidance and support during the(More)
Local mesh-refining algorithms known from adaptive finite element methods are adopted for locally conservative and monotone finite volume discretizations of boundary value problems for steady-state convection-diffusion-reaction equations. The paper establishes residual-type explicit error estimators and averaging techniques for a posteriori finite volume(More)
The behavior of many physical processes is greatly aaected by some of their localized physical properties. For such cases it is essential that local grid reenement techniques be applied. We present the results of implementation of four local error indicators, namely the residual based error indicator, an error indicator based on the approximation of the(More)
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