1,474 research outputs found
Multi-goal oriented a posteriori error estimates for nonlinear partial differential equations
No full textPartial differential equations (PDEs) play an important role in many applications. However, the solutions to these PDEs are known in rare cases. Thus, the partial differential equations must be approximated by some discretization techniques like the Finite Element Method (FEM) leading to approximate solutions. In practice, often the solution is not of primary interest, but some goal functional (quantity of interest). These quantitites of interest are, e.g., mean value flux and point evaluations provided that they exist. For instance, for the Navier-Stokes equations, these goal functionals could be pressure difference, drag and lift. Moreover, there may be several quantities of interest in practical applications. In this thesis, we extend the dual weighted residual method to multiple goal functionals at once in a cost efficient way. The dual weighted residual method gives information on the sensitivity of the goal functionals, and allows us to estimate the error at the same time. This leads to a posteriori error estimates for multiple goal functionals and to a corresponding Adaptive Finite Element Method (AFEM) aiming at the accurate computation of all goal functionals at once. Furthermore, we extend the methodology to optimal control problem subject to some nonlinear PDE constraint. Here, a reduced optimization problem is formulated in terms of the control variable. Moreover, we derive two-sided bounds for the goal oriented error estimates for higher-order approximation and interpolation. Using a saturation assumption, we derive lower bounds yielding the efficiency of the error estimator. These results hold true in the case of nonlinear PDEs and nonlinear goal functionals. We also perform careful studies of the remainder term that is usually neglected. Based on these theoretical investigations, several algorithms are designed.submitted by Dipl.-Ing. Endtmayer BernhardDissertation Universität Linz 202
Bernhard Karlgren Portrait of A Scholar
No full textThe author draws a portrait of his teacher Bernhard Karlgren (1889-1978), whose research in a variety of fields laid the foundations of Modern Sinology. The work deals with Karlgren's childhood, school years, university studies at Uppsala and St. Petersburg, adventurous sojourn in China, studies in Paris, and academic career at Uppsala and Gothenburg University. This book will help the reader gain insight into the man behind the stern scholar.Intro -- Preface -- 1 Childhood and Schooldays in Jönköping, 1889-1907 -- THE HOME AND THE FAMILY -- LARS OF THE MANOR AND HIS TWO SONS -- THE CLERGYMAN'S DAUGHTER ELLA HASSELBERG AND HER FAMILY -- THE GOOD AND FAITHFUL SERVANT -- THE DIFFICULT YEARS -- BERNHARD: POET, TRANSLATOR, AND DRAMATIST -- THE DIALECT INVESTIGATOR -- 2 Liber Studiosus, 1907-1909 -- STUDIES AT UPPSALA UNIVERSITY -- RUSSIAN WINTER -- 3 The Great Adventure, 1910-1911 -- SAILING IN A SHIP CARRYING GUNPOWDER AS CARGO -- TAIYUAN UNIVERSITY -- THE INDUSTRIOUS DIALECTOLOGIST -- WORRIES ABOUT THE FUTURE -- THE TREASURES OF THE STONE FOREST -- THE FOREIGN CORRESPONDENT -- 4 The Irresolute Strategist, 1912-1914 -- THE INTERLUDE IN LONDON -- AT THE FEET OF CHAVANNES IN PARIS -- 5 The Diligent Correspondent -- THE AVID READER -- THE GREAT QUESTIONS -- SELF-SEARCHING -- 6 The Scholarly Breakthrough -- UPPSALA OR PARIS? -- THE PUBLIC DEFENSE OF THE THESIS -- THE YOUNG LECTURER -- THE STRUGGLE TO MAKE A LIVING -- THE FARSIGHTED PLANNER -- 7 The Gothenburg Years, 1918-1939 -- THE FIRST YEARS AT GOTHENBURG UNIVERSITY -- BACK TO THE FAR EAST -- BACK AT THE TEACHER'S DESK -- THE NARROW CONFINES OF THE SOCIETY OF SCHOLARSHIP -- THE CONFERRING OF DOCTORAL DEGREES IN 1931 -- BERNHARD KARLGREN AND SVEN HEDIN 9 -- THE DEFENDER OF HUMAN RIGHTS -- BERNHARD KARLGREN OUTSIDE THE IVORY TOWER -- 8 Proximitatem Linguae Longinquae Manifestam Fecit -- CHINA'S TRADITIONAL PHILOLOGY -- LINGUISTIC ECHO-SOUNDING -- RIMES AND SOUNDING SIGNS IN ANCIENT CHINA -- SIBLINGS IN FAMILIES OF CHINESE WORDS -- THE BOLD PIONEER -- UNFINISHED INCEPTIONS -- ABC TRAVELS EAST -- 9 Stockholm, 1939-1959: The Legendary Master -- THE EAST ASIAN COLLECTION -- THE MORPHOLOGY AND SYNTAX OF BRONZE DÉCOR -- THE PHILOLOGIST IN HIS ELEMENT -- EXCURSIONS IN CHINESE GRAMMAR -- THE STERN CRITIC -- THE EMINENT POPULARIZERSCHOLAR IN THE SERVICE OF SOCIETY -- DR. BACKMAN, DOCENT SPIRA, AND SENIOR MASTER BRUUN -- A REMARKABLE FAMILY OF BROTHERS AND SISTERS -- THE VENERATED MASTER AND HIS DISCIPLES -- 10 Bernhard Karlgren, Professor Emeritus, 1959-1978 -- BERNHARD KARLGREN AND THE BMFEA -- IN THE LEXICOGRAPHER'S STUDY -- CITIZEN IN THE REPUBLIC OF SCHOLARS -- A List of Works by Bernhard Karlgren in Other Languages than Swedish, Together with Translations into Chinese and Japanese, and a List of His Distinctions and Awards -- ABBREVIATIONS -- Notes -- CHAPTER 1. CHILDHOOD -- CHAPTER 2. LIBER STUDIOSUS -- CHAPTER 3. THE GREAT ADVENTURE -- CHAPTER 4. IRRESOLUTE STRATEGIST -- CHAPTER 5. DILIGENT CORRESPONDENT -- CHAPTER 6. SCHOLARLY BREAKTHROUGH -- CHAPTER 7. GOTHENBURG YEARS -- CHAPTER 8. PROXIMITATEM LINGUAE -- CHAPTER 9. STOCKHOLM, 1939-1959 -- CHAPTER 10. PROFESSOR EMERITUS -- BibliographyThe author draws a portrait of his teacher Bernhard Karlgren (1889-1978), whose research in a variety of fields laid the foundations of Modern Sinology. The work deals with Karlgren's childhood, school years, university studies at Uppsala and St. Petersburg, adventurous sojourn in China, studies in Paris, and academic career at Uppsala and Gothenburg University. This book will help the reader gain insight into the man behind the stern scholar.Description based on publisher supplied metadata and other sources.Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, YYYY. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Bernhardi Kellii Hypodidascalus : Darin zu sehen Wie die Schulemeister und Eltern ire angehende Kinder ohn viel schlege durch mannigerlei Richtwege auffs beste/ rechtste und leichtste Teutsch und Lateinisch lesen und schreiben lernen mügen ; Mit einer vorrede und zu End angehengten Ethica scholastica ...
No full textAdaptive Mesh Refinement for Multiple Goal Functionals
No full textIn practical applications, one is often not interested in the entire solution of a partial differential equation, but in a special quantity of interest, which depends on the solution. Since in general, we cannot find the solution of the partial differential equation exactly and we have to construct a numerical approximation. This leads to an inaccuracy in the quantity of interest as well. Now one could think about just trying to increase the accuracy in our quantity of interest and not in the entire solution. This can be achieved by applying adaptive mesh refinement with respect to the quantity of interest. One possibility of such a technique is the dual weighted residual method based on an error estimator with a variational localization via a partition of unity. Therein, local cell residuals are weighted by a localized adjoint solution. However, there can be more than one quantity of interest. In this thesis, we will discuss how the dual weighted residual method can be applied to several goal functionals at once. We will investigate algorithmic techniques to formulate and solve such a multiple goal functionals problem. A naive approach would be solve to each goal functional one adjoint problem, which is computationally costly. Rather, we adopt a dual-dual problem, which yields an adjoint state by just two additional solves. The key result of this thesis is a new procedure to solve the dual-dual problem. In the numerical examples, we show how the different quantities of interest affect each other, and in which situations our new method leads to an improvement in comparison with global refinement.In der praktischen Anwendung von partiellen Differentialgleichungen ist man oft nicht an der Lösung selbst interessiert, sondern nur an einem bestimmten Wert (eines sogenannten Zielfunktionals), der von der Lösung abhangt. Da im Allgemeinen partielle Differentialgleichungen nicht analytisch lösbar sind, können wir die Lösung nur mit einer Naherungslösung approximieren. Diese Ungenauigkeit liefert auch einen Fehler im gesuchten Wert des Zielfunktionals. Man könnte nun versuchen nur die Fehler in dem Zielfunktional zu reduzieren und nicht den Fehler in der Lösung selbst. Eine Möglichkeit, dies zu realisieren, ist die ziel-orientierte a posteriori Fehlerschatzung mit dual gewichteten Residuen, wobei eine variationelle Lokalisierung durch eine Zerlegung der Eins realisiert wird. In vielen Anwendungen sind jedoch mehrere Zielfunktionale von Interesse. In dieser Arbeit wird beschrieben wie die ziel-orientierte a posteriori Fehlerschatzung mit dual gewichteten Residuen auf mehrere Zielfunktionale gleichzeitig angewendet werden kann. Natürlich kann man den Fehlerschatzer für jeden dieser Werte gesondert berechnen und diese spater addieren. Dies resultiert jedoch in einem sehr hohen Rechenaufwand, da wir für jeden Wert ein adjungiertes Problem lösen müssen. Um dies zu vermeiden, wird stattdessen ein dual-duales Problem gelöst. Hier muss immer nur doppelt so oft gelöst werden, als für einen Wert. Das Hauptresultat dieser Arbeit besteht in der Konstruktion und Analyse eines verbesserten Algorithmus zur Lösung des dual-dualen Problems. In unseren Ergebnissen versuchen wir herauszufinden wie die Werte einander beeinflussen und auch wann diese Methode einen Vorteil gegenüber globaler Verfeinerung liefert.submitted by Endtmayer BernhardMasterarbeit Universität Linz 201
Adaptive Mesh Refinement for Multiple Goal Functionals
No full textIn practical applications, one is often not interested in the entire solution of a partial differential equation, but in a special quantity of interest, which depends on the solution. Since in general, we cannot find the solution of the partial differential equation exactly and we have to construct a numerical approximation. This leads to an inaccuracy in the quantity of interest as well. Now one could think about just trying to increase the accuracy in our quantity of interest and not in the entire solution. This can be achieved by applying adaptive mesh refinement with respect to the quantity of interest. One possibility of such a technique is the dual weighted residual method based on an error estimator with a variational localization via a partition of unity. Therein, local cell residuals are weighted by a localized adjoint solution. However, there can be more than one quantity of interest. In this thesis, we will discuss how the dual weighted residual method can be applied to several goal functionals at once. We will investigate algorithmic techniques to formulate and solve such a multiple goal functionals problem. A naive approach would be solve to each goal functional one adjoint problem, which is computationally costly. Rather, we adopt a dual-dual problem, which yields an adjoint state by just two additional solves. The key result of this thesis is a new procedure to solve the dual-dual problem. In the numerical examples, we show how the different quantities of interest affect each other, and in which situations our new method leads to an improvement in comparison with global refinement.In der praktischen Anwendung von partiellen Differentialgleichungen ist man oft nicht an der Lösung selbst interessiert, sondern nur an einem bestimmten Wert (eines sogenannten Zielfunktionals), der von der Lösung abhangt. Da im Allgemeinen partielle Differentialgleichungen nicht analytisch lösbar sind, können wir die Lösung nur mit einer Naherungslösung approximieren. Diese Ungenauigkeit liefert auch einen Fehler im gesuchten Wert des Zielfunktionals. Man könnte nun versuchen nur die Fehler in dem Zielfunktional zu reduzieren und nicht den Fehler in der Lösung selbst. Eine Möglichkeit, dies zu realisieren, ist die ziel-orientierte a posteriori Fehlerschatzung mit dual gewichteten Residuen, wobei eine variationelle Lokalisierung durch eine Zerlegung der Eins realisiert wird. In vielen Anwendungen sind jedoch mehrere Zielfunktionale von Interesse. In dieser Arbeit wird beschrieben wie die ziel-orientierte a posteriori Fehlerschatzung mit dual gewichteten Residuen auf mehrere Zielfunktionale gleichzeitig angewendet werden kann. Natürlich kann man den Fehlerschatzer für jeden dieser Werte gesondert berechnen und diese spater addieren. Dies resultiert jedoch in einem sehr hohen Rechenaufwand, da wir für jeden Wert ein adjungiertes Problem lösen müssen. Um dies zu vermeiden, wird stattdessen ein dual-duales Problem gelöst. Hier muss immer nur doppelt so oft gelöst werden, als für einen Wert. Das Hauptresultat dieser Arbeit besteht in der Konstruktion und Analyse eines verbesserten Algorithmus zur Lösung des dual-dualen Problems. In unseren Ergebnissen versuchen wir herauszufinden wie die Werte einander beeinflussen und auch wann diese Methode einen Vorteil gegenüber globaler Verfeinerung liefert.submitted by Endtmayer BernhardMasterarbeit Universität Linz 201
Bernhard Boyneburg (Barber) Collection ca. 1919-1975
No full textThe collection contains handwritten and typed manuscripts of essays by Bernhard Boyneburg about Richard Wagner and various other topics. Also included is the copy of a letter from the International Tracing Service of the Red Cross about the fate of Bernhard Barber, his wife and his son.Sophie B. Mann, October 2002Bernhard Barber was an author who published political and philosophical works under the name Boyneburg. He was born 1874 in Leipzig, but lived and worked in Vienna. In 1941, he, his wife Olga née Prager (b. 1897) and their son Eduard Fritz (b. 1905) were deported to the Ghetto in Lodz, where they perished. Barberâs daughter Sophie Mann survived the Holocaust.Bernhard Boyneburg''s published works include ,Die Despotie der Mittel, ihre Erkenntnis : die Grundlage rascher Voelkerversoehnung, Anzengruber, Wien 1919, and ,Der Weg aus dem Chaos: Neues zum Satze von der Despotie der Mittel, Amalthea, Zürich etc., 1927'.digitize
Heldenplatz by Thomas Bernhard
No full textopenL’opera teatrale Heldenplatz è l’ultima e tra le più importanti dello scrittore e drammaturgo austriaco Thomas Bernhard, pubblicata e rappresentata nel 1988. Il testo provocò uno scandalo in Austria ancora prima di essere messo in scena, poiché presenta critiche verso la società austriaca del secondo dopoguerra, ritenuta da Bernhard colpevole di non aver affrontato il proprio passato nazionalsocialista. Questa vicenda conferma la visione di Bernhard e dimostra l'importanza del teatro per la società.The play Heldenplatz is the last and one of the most important plays by the Austrian author Thomas Bernhard, and it was published and performed in 1988. It caused a scandal in Austria even before its release due to the presence of critical assertions regarding Austrian post-war society in the text. According to Bernhard, that society had not dealt with its nazist past. This reaction shows Bernhard's view to be correct and it highlights the importance of theatre for society
Classification of medicinal plants based on near-infrared spectroscopy data
No full textauthor: Bernhard HuberMasterarbeit Universität Innsbruck 202
About twin primes and distribution of primes
No full textThis paper give us a demonstration of twin primes conjecture using approximation of function �(iupsilon) that we introduce in section 6. Section 1-5 give us introduction to terminology and a clarification on (iupsilon) terms. In particular section
5 is really important because of its Lemma. Section 7 reassume foregoing explanations and it give us two theorems and one corollary;the theorem 7.2 give us exact approximation of twin primes counting function
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