Graded Finite Element Methods For Elliptic Problems In Nonsmooth Domains
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Graded Finite Element Methods for Elliptic Problems in Nonsmooth Domains
This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.
FlexPDE and Finite Element Method Applications in Thermal Energy Storage and Cavities
Author: Hosseinzadeh, Khashayar
language: en
Publisher: IGI Global
Release Date: 2024-03-01
Academic scholars are increasingly confronted with the complex challenges of understanding and optimizing heat transfer processes, particularly in the areas of cavities and Phase Change Materials (PCM). These issues are central to a range of crucial applications, including building systems, electronic equipment, and the harnessing of solar energy. The need for innovative solutions to enhance heat transfer efficiency is more pressing than ever, and a comprehensive resource to guide scholars through these complexities is essential. FlexPDE and Finite Element Method Applications in Thermal Energy Storage and Cavities is research book specifically designed to provide scholars with the knowledge and expertise necessary to navigate the complexities of heat transfer issues. With a strong emphasis on practical application, the book leverages the capabilities of the Finite Element Method (FEM) through the FLEXPDE software, making it a valuable resource for those seeking innovative solutions to problems in heat transfer.
Boundary Element Topics
Author: W.L. Wendland
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The so-called boundary element methods BEM, i.e. finite element approxima tions of boundary integral equations have been improved recently even more vividly then ever before and found some remarkable support by the German Research Foundation DFG in the just finished Priority Research Program "boundary element methods" . When this program began, we could start from several already existing particular activities which then during the six years initiated many new re sults and decisive new developments in theory and algorithms. The program was started due to encouragement by E. Stein, when most of the later par ticipants met in Stuttgart at a Boundary Element Conference 1987. Then W. Hackbusch, G. Kuhn, S. Wagner and W. Wendland were entrusted with writing the proposal which was 1988 presented at the German Research Foun dation and started in 1989 with 14 projects at 11 different universities. After German unification, the program was heavily extended by six more projects, four of which located in Eastern Germany. When we started, we were longing for the following goals: 1. Mathematicians and engineers should do joint research. 2. Methods and computational algorithms should be streamlined with re spect to the new computer architectures of vector and parallel computers. 3. The asymptotic error analysis of boundary element methods should be further developed. 4. Non-linear material laws should be taken care of by boundary element methods for crack-mechanics. 5. The coupling of finite boundary elements should be improved.