Shock Capturing and High-Order Methods for Hyperbolic Conservation Laws (Paperback)

Jan Glaubitz

ISBN 10: 3832550844 / ISBN 13: 9783832550844

Published by Logos Verlag Berlin GmbH, Berlin, 2020

About this Item

Paperback. This thesis is concerned with the numerical treatment of hyperbolic conservation laws. These play an important role in describing many natural phenomena. Challenges in their theoretical as well as numerical study stem from the fact that spontaneous shock discontinuities can arise in their solutions, even in finite time and smooth initial states.Moreover, the numerical treatment of hyperbolic conservations laws involves many different fields from mathematics, physics, and computer science. As a consequence, this thesis also provides contributions to several different fields of research -- which are still connected by numerical conservation laws, however. These contributions include, but are not limited to, the construction of stable high order quadrature rules for experimental data, the development of new stable numerical methods for conservation laws, and the investigation and design of shock capturing procedures as a means to stabilize high order numerical methods in the presence of (shock) discontinuities. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783832550844

Bibliographic Details

• Title: Shock Capturing and High-Order Methods for Hyperbolic Conservation Laws (Paperback)
• Publisher: Logos Verlag Berlin GmbH, Berlin
• Publication Date: 2020
• Language: English
• ISBN 10: 3832550844
• ISBN 13: 9783832550844
• Binding: Paperback
• Condition: new

About this title

Synopsis

This thesis is concerned with the numerical treatment of hyperbolic conservation laws. These play an important role in describing many natural phenomena. Challenges in their theoretical as well as numerical study stem from the fact that spontaneous shock discontinuities can arise in their solutions, even in finite time and smooth initial states. Moreover, the numerical treatment of hyperbolic conservations laws involves many different fields from mathematics, physics, and computer science. As a consequence, this thesis also provides contributions to several different fields of research - which are still connected by numerical conservation laws, however. These contributions include, but are not limited to, the construction of stable high order quadrature rules for experimental data, the development of new stable numerical methods for conservation laws, and the investigation and design of shock capturing procedures as a means to stabilize high order numerical methods in the presence of (shock) discontinuities. Jan Glaubitz was born in Braunschweig, Germany, in 1990 and completed his mathematical studies (B.Sc., 2014, M.Sc., 2016, Dr. rer. nat., 2019) at TU Braunschweig. In 2016, he received awards from the German Mathematical Society (DMV) for his master's thesis as well as from the Society of Financial and Economic Mathematics of Braunschweig (VBFWM). In 2017, he was honored with the teaching award "LehrLEO" for the best tutorial at TU Braunschweig. Since 2020, he holds a position as a postdoctoral researcher at Dartmouth College, NH, USA.