Convergence of a second-order energy-decaying method for the viscous rotating shallow water equation

Georgios Akrivis, Buyang Li, Jilu Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review


An implicit energy-decaying modified Crank-Nicolson time-stepping method is constructed for the viscous rotating shallow water equation on the plane. Existence, uniqueness, and convergence of semidiscrete solutions are proved by using Schaefer's fixed point theorem and H2 estimates of the discretized hyperbolic-parabolic system. For practical computation, the semidiscrete method is further discretized in space, resulting in a fully discrete energy-decaying finite element scheme. A fixed-point iterative method is proposed for solving the nonlinear algebraic system. The numerical results show that the proposed method requires only a few iterations to achieve the desired accuracy, with second-order convergence in time, and preserves energy decay well.

Original languageEnglish
Pages (from-to)265-288
Number of pages24
JournalSIAM Journal on Numerical Analysis
Issue number1
Publication statusE-pub ahead of print - 26 Jan 2021


  • Energy decay
  • Error estimate
  • Modified Crank-Nicolson
  • Viscous shallow water equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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