Τίτλος:
On the standard Galerkin method with explicit RK4 time stepping for the shallow water equations
Γλώσσες Τεκμηρίου:
Αγγλικά
Περίληψη:
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 four-stage, fourth 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. © 2020 Oxford University Press. All rights reserved.
Συγγραφείς:
Antonopoulos, D.C.
Dougalis, V.A.
Kounadis, G.
Περιοδικό:
IMA Journal of Numerical Analysis
Εκδότης:
Oxford University Press
Λέξεις-κλειδιά:
Finite element method; Galerkin methods; Initial value problems; Mesh generation; Runge Kutta methods, Error estimates; Explicit Runge-Kutta methods; Finite element space; Fourth order four-stage explicit runge-kuttum method; Fourth-order; Galerkin finite element methods; Shallow water equations; Simple++; Standard galerkin finite element method; Time-stepping, Equations of motion
DOI:
10.1093/IMANUM/DRZ033
