Higher-Order Finite Element Methods provides an exhaustive survey of intrinsic techniques and practical implementation of higher-order finite element schemes. It addresses automatic hp-adaptivity in one and two spatial dimensions and includes up-to-date references to ongoing research related to automatic hp-adaptivity in 3D. The authors' discussion of suitable data structures and efficient linear solvers provides an excellent introduction to key, often neglected aspects of this class of methods. Avoiding heavy mathematical jargon where possible, the book is clear, comprehensive, and designed for both applied mathematicians and engineers who are interested in finite elements.

Pavel Solin, Karel Segeth, Ivo Dolezel

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

Introduction. Hierarchic Master Elements of Arbitrary Order. Higher-Order Finite Element Discretization. Higher-Order Numerical Quadrature. Numerical Solution of Finite Element Equations. Mesh Optimization, Reference Solutions, and hp-Adaptivity.