Inside finite elements (Q2797266)

This book discusses ``the algorithmic realization of finite element methods for partial differential equations (PDEs)''. It ``complements general textbooks on numerical analysis of PDEs''. The algorithms presented in the book are implemented in Matlab. The book is divided into 9 chapters. Chapter 1 briefly discusses the basic concepts of finite elements. In Chapter, 2 the author analyzes ``the grids, their creation and representation'' and the ``finite element functions defined on grids and their visualization''. Chapter 3 discusses ``the assembly process, building up Galerkin systems from elemental matrices derived analytically''. In Chapter 4, the author ``covers classical direct and iterative solvers''. Chapter 5 discusses ``hierarchical error estimation with quadratic bubble functions''. Chapter 6 deals with mesh refinement and Chapter 7 introduces the multigrid concept. Chapter 8 and 9 present applications of the finite element method in elasticity and in fluid mechanics, respectively.NEWLINENEWLINEAfter reading this book, one should be able to write his own code ``capable of solving stationary and time-harmonic, scalar and vectorial problems on adaptively refined meshes with multigrid efficiency''.NEWLINENEWLINEThis book is a ``must have'' for mathematicians and engineers interested in scientific computing and applied mathematics. It is an excellent guide in the field of applied finite elements that is absolutely necessary for a deeper understanding of the details of numerical implementation of the finite element method. The book very successfully complements the general textbooks on numerical analysis and PDEs.