Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; 1: Introduction and overview; 1.1 Typical problems where convection-diffusion occurs; 1.2 Model problems; 1.3 Numerical difficulties with simple difference schemes; 1.3.1 Central difference scheme; 1.3.2 Upwind difference scheme; 1.3.3 Truncation error and global error; 1.3.4 Graded meshes; 1.4 Finite elements in one dimension; 1.4.1 Discrete equations for piecewise linear approximation; 1.4.2 Outline error analysis; 1.4.3 Unsteady problems; 1.4.4 A posteriori error analysis
متن يادداشت
1.5 Iterative solution of discrete equations1.6 Overview of effective methods; 2: Selected results from mathematical analysis; 2.1 Introduction; 2.2 Maximum principles; 2.3 Boundary and interior layers in one dimension; 2.3.1 Problems with no turning points; 2.3.2 Turning point problems; 2.4 Derivative bounds in a one-dimensional boundary layer; 2.5 Weak formulation of the problem; 2.6 A priori bounds and boundary layers in two dimensions; 2.7 Green's functions; 2.7.1 One-dimensional examples; 2.7.2 Free-space Green's functions; 3: Difference schemes for steady problems
متن يادداشت
3.1 One-dimensional problems3.2 Hermitian and Operator Compact Implicit (OCI) schemes; 3.2.1 Derivation of the standard scheme; 3.2.2 Properties of OCI and related schemes; 3.2.3 Generalised OCI schemes; 3.3 Exponential fitting and locally exact schemes; 3.3.1 Exponentially fitted schemes; 3.3.2 Locally exact schemes; 3.4 Error analysis by a maximum principle; 3.4.1 The simple upwind scheme; 3.4.2 The Allen and Southwell scheme; 3.4.3 Exponential fitting and uniform error bounds; 3.5 Turning point problems; 3.6 Simple extensions to two dimensions; 3.6.1 Maximum principles
متن يادداشت
3.6.2 Typical difference schemes and error bounds3.6.3 Crosswind diffusion; 3.6.4 Adaptive and nonlinear difference schemes; 4: Finite element methods: Galerkin schemes; 4.1 Triangular and quadrilateral meshes; 4.1.1 Local mapping for a triangle; 4.1.2 Local mapping for a quadrilateral; 4.2 Standard error bounds for Galerkin schemes; 4.2.1 Approximation properties of the trial spaces; 4.2.2 A general error bound; 4.2.3 Inverse estimates for the trial spaces; 4.3 Galerkin methods on a triangular mesh; 4.3.1 Linear approximation; 4.3.2 Quadratic approximation
متن يادداشت
4.4 Galerkin methods on quadrilaterals4.4.1 Isoparametric bilinear approximation; 4.4.2 Biquadratic approximation; 4.5 Comparative approximation properties; 4.6 Numerical comparisons of accuracy; 4.6.1 One dimension, constant b; 4.6.2 A one-dimensional conservation law; 4.6.3 The first IAHR/CEGB problem; 5: Petrov-Galerkin methods; 5.1 Upwinded test functions; 5.2 Approximate symmetrization; 5.2.1 Symmetrization based on B1(. , .); 5.2.2 Symmetrization based on B2 (. , .); 5.3 Hemker test functions; 5.4 Error bounds in L ∝, and L2 norms; 5.5 Streamline diffusion methods
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ویراست دیگر از اثر در قالب دیگر رسانه
عنوان
Revival: Numerical Solution of Convection-Diffusion Problems (1996).
شماره استاندارد بين المللي کتاب و موسيقي
9781138561038
نام شخص به منزله سر شناسه - (مسئولیت معنوی درجه اول )