Lutz Angermann Knihy

Focusing on numerical methods for elliptic and parabolic partial differential equations, this graduate-level text integrates theory with practical applications. It explores finite difference, finite element, and finite volume methods, while addressing modern topics like adaptive and multilevel methods. The second edition expands on mixed discretization, broader applications, and enhanced techniques for convection-dominated problems. It serves as a comprehensive resource for mathematics, engineering, and physics students, guiding them in method selection and finite element programming.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in - search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as nume- cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.