Resumen

Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation points and corners) meet it. The amplitude of these waves is determined, and the implications are considered for many quite general flows. The asymptotic results are compared to numerical simulations of the full problem for flow over a polygonal plough and for flow round a right-angled corner, and they show remarkably good agreement, even for quite large values of the surface tension parameter.

 

Computation of Periodic Solution Bifurcations in ODEs Using Bordered Systems. E. J. Doedel, W. Govaerts, Yu. A. Kuznetsov (Pages 401-435)

The P₁^mod Element: A New Nonconforming Finite Element for Convection-Diffusion Problems. Petr Knobloch, Lutz Tobiska (Pages 436-456)

Approximation of Time-Dependent Viscoelastic Fluid Flow: SUPG Approximation. Vincent J. Ervin, William W. Miles (Pages 457-486)

Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws. Huazhong Tang, Tao Tang (Pages 487-515)

On the Convergence of Difference Schemes for Hyperbolic Problems with Concentrated Data. Bosko S. Jovanovic, Lubin G. Vulkov  (Pages 516-538)

H-Convergence and Numerical Schemes for Elliptic Problems. Robert Eymard, Thierry Gallouët (Pages 539-562)

Numerical Approximation of the Lifshitz--Slyozov--Wagner Equation. Francis Filbet, Philippe Laurençot (Pages 563-588)

A Preconditioned Conjugate Gradient Method for Nonselfadjoint or Indefinite Orthogonal Spline Collocation Problems. Rakhim Aitbayev, Bernard Bialecki (Pages 589-604)

Monotonicity-Preserving Linear Multistep Methods. Willem Hundsdorfer, Steven J. Ruuth, Raymond J. Spiteri (Pages 605-623)

P₁-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems. Chunjae Park, Dongwoo Sheen (Pages 624-640)

Space Localization and Well-Balanced Schemes for Discrete Kinetic Models in Diffusive Regimes. Laurent Gosse, Giuseppe Toscani  (Pages 641-658)

Optimal Error Estimates of the Chebyshev--Legendre Spectral Method for Solving the Generalized Burgers Equation. Hua Wu, Heping Ma, Huiyuan Li (Pages 659-672)

Fast Sweeping Algorithms for a Class of Hamilton--Jacobi Equations. Yen-Hsi Richard Tsai, Li-Tien Cheng, Stanley Osher, Hong-Kai Zhao (Pages 673-694)

The Postprocessing Galerkin and Nonlinear Galerkin Methods---A Truncation Analysis Point of View. Len G. Margolin, Edriss S. Titi, Shannon Wynne  (Pages 695-714)

First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity. Zhiqiang Cai, Gerhard Starke (Pages 715-730)

Conditioning of Hierarchic p-Version Nédélec Elements on Meshes of Curvilinear Quadrilaterals and Hexahedra. Mark Ainsworth, Joe Coyle (Pages 731-750)

Polynomial Interpolation on the Unit Sphere. Yuan Xu (Pages 751-766)

Semicirculant Preconditioning of Elliptic Operators. Sang Dong Kim, Seymour V. Parter (Pages 767-795)

Corrigendum: Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals. Qiang Du, Benyu Guo, Jie Shen (Pages 796-798)