The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and

Higher-Order Finite Element Methods. Chapman and Hall/CRC. 2003.

Ŝolín, Pavel

Chapman & Hall/CRC

A modern presentation of integral methods in low-frequencyelectromagnetics This book provides state-of-the-art knowledge on integralmethods in low-frequency electromagnetics. Blending theory withnumerous examples, it introduces key aspects of the integralmethods used in engineering as a powerful alternative to PDE-basedmodels. Readers will get complete coverage of:The electromagnetic field and its basic characteristicsAn overview of solution methodsSolutions of electromagnetic fields by integral expressionsIntegral and integrodifferential methodsIndirect solutions of electromagnetic fields by the boundaryelement methodIntegral equations in the solution of selected coupledproblemsNumerical methods for integral equationsAll computations presented in the book are done by means of theauthors' own codes, and a significant amount of their own resultsis included. At the book's end, they also discuss novel integraltechniques of a higher order of accuracy, which are representativeof the future of this rapidly advancing field.Integral Methods in Low-Frequency Electromagnetics is ofimmense interest to members of the electrical engineering andapplied mathematics communities, ranging from graduate students andPhD candidates to researchers in academia and practitioners inindustry.

Integral Methods in Low-Frequency Electromagnetics

Computers & Technology

Dolezel, Ivo

Karban, Pavel

Ulrych, Bohus

Programming

Wiley-Interscience

A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM. A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM. Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science. Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.

Partial Differential Equations and the Finite Element Method

Science & Math

Mathematics

The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales. 
Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity. 
Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.

Higher-Order Finite Element Methods (Studies in Advanced Mathematics)

Segeth, Karel

Computer Science

Chapman and Hall/CRC

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