{
  "id": "1810.11008",
  "version": "v1",
  "published": "2018-10-25T17:55:20.000Z",
  "updated": "2018-10-25T17:55:20.000Z",
  "title": "On the standard Galerkin method with explicit RK4 time stepping for the Shallow Water equations",
  "authors": [
    "D. c. Antonopoulos",
    "V. a. Dougalis",
    "G. Kounadis"
  ],
  "comment": "24 pages, 5 tables",
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension. We discretize the problem in space by the standard Galerkin finite element method on a quasiuniform mesh and in time by the classical 4-stage, 4th order, explicit Runge-Kutta scheme. Assuming smoothness of solutions, a Courant number restriction, and certain hypotheses on the finite element spaces, we prove L2 error estimates that are of fourth-order accuracy in the temporal variable and of the usual, due to the nonuniform mesh, suboptimal order in space. We also make a computational study of the numerical spatial and temporal orders of convergence, and of the validity of a hypothesis made on the finite element spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-25T17:55:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M60",
      "65M12"
    ],
    "keywords": [
      "shallow water equations",
      "explicit rk4 time stepping",
      "standard galerkin method",
      "galerkin finite element method",
      "finite element spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}