Frontiers in Numerical Analysis - Durham 2010
James Blowey, Max Jensen
Springer Science & Business Media, Jan 10, 2012 - Mathematics - 292 pages
This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.
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ˆ ˆ ˆ algorithm Anal applied bilinear form boundary conditions C0 interior penalty Cauchy-Schwarz inequality convergence defined degrees of freedom denote derivative discontinuous Galerkin methods discrete problem Domain Decomposition Domain Decomposition Methods edge elements ee &h eigenfunction eigenvalue problem electromagnetic elliptic problems error analysis finite element approximation finite element method finite element space formulation Fourier-Laplace function Galerkin method grid higher order inequality integral equations interface interior penalty methods inverse L2-norm Lagrange finite element Lagrange multipliers Laplace Lemma linear Math matrix Maxwell’s equations multigrid Multigrid Methods Nitsche’s method Numer obtain orthogonal Partial Differential Equations penalty term piecewise polynomial posteriori error estimates preconditioner Proof regularity S.C. Brenner satisfies scheme second order Sect SIAM Sobolev space solution solve source problem stabilisation stability standard symmetric techniques Theorem timestep triangle V-cycle vector wave equation