By Sören Bartels (auth.)

Finite aspect equipment for approximating partial differential equations have reached a excessive measure of adulthood, and are an indispensible instrument in technology and know-how. This textbook goals at supplying a radical creation to the development, research, and implementation of finite aspect tools for version difficulties coming up in continuum mechanics. the 1st a part of the booklet discusses ordinary houses of linear partial differential equations besides their simple numerical approximation, the functional-analytical framework for carefully setting up lifestyles of options, and the development and research of easy finite aspect equipment. the second one half is dedicated to the optimum adaptive approximation of singularities and the quick iterative answer of linear platforms of equations coming up from finite aspect discretizations. within the 3rd half, the mathematical framework for studying and discretizing saddle-point difficulties is formulated, corresponding finte point equipment are analyzed, and specific functions together with incompressible elasticity, skinny elastic gadgets, electromagnetism, and fluid mechanics are addressed. The ebook comprises theoretical difficulties and functional tasks for all chapters, and an creation to the implementation of finite aspect methods.