Galerkin finite element methods for two-dimensional RLW and SRLW equations

ABSTRACT

In this paper, Galerkin finite methods for two-dimensional regularized long wave and symmetric regularized long wave equation are studied. The discretization in space is by Galerkin finite element method and in time is based on linearized backward Euler formula and extrapolated Crank–Nicolson scheme. Existence and uniqueness of the numerical solutions have been shown by Brouwer fixed point theorem. The error estimates of linearlized Crank–Nicolson method for RLW and SRLW equations are also presented. Numerical experiments, including the error norms and conservation variables, verify the efficiency and accuracy of the proposed numerical schemes.

KEYWORDS:

• RLW equation
• SRLW equation
• finite element method
• backward Euler formula
• extrapolated Crank–Nicolson method

AMS SUBJECT CLASSIFICATIONS:

• 65M12
• 65M60
• 35Q55
• 26B35
• 65Z05

Disclosure statement

No potential contact of interest was reported by the authors.

Additional information

Funding

The work was supported by supported by CSC of China (201506280175) and NSF of China (11371289, 11501441).