Higher-Order Finite Element Methods

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.