{
  "id": "1008.4248",
  "version": "v1",
  "published": "2010-08-25T10:36:10.000Z",
  "updated": "2010-08-25T10:36:10.000Z",
  "title": "Notes on error estimates for Galerkin approximations of the 'classical' Boussinesq system and related hyperbolic problems",
  "authors": [
    "D. C. Antonopoulos",
    "V. A. Dougalis"
  ],
  "comment": "61 pages, 2 figures, 12 tables",
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider the `classical' Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform horizontal channel. We discretize an initial-boundary-value problem for these systems in space using Galerkin-finite element methods and prove error estimates for the resulting semidiscrete problems and also for their fully discrete analogs effected by explicit Runge-Kutta time-stepping procedures. The theoretical orders of convergence obtained are consistent with the results of numerical experiments that are also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-25T10:36:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "35Q53"
    ],
    "keywords": [
      "related hyperbolic problems",
      "boussinesq system",
      "error estimates",
      "galerkin approximations",
      "systems model two-way propagation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.4248A"
    }
  }
}