A Crank‐Nicolson Petrov‐Galerkin method with quadrature for semi‐linear parabolic problems | Zendy

Bialecki B. | Zendy; Ganesh M. | Zendy; Mustapha K. | Zendy

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A Crank‐Nicolson Petrov‐Galerkin method with quadrature for semi‐linear parabolic problems

Author(s) -

Bialecki B.,

Ganesh M.,

Mustapha K.

Publication year - 2005

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.20068

Subject(s) - petrov–galerkin method , mathematics , discretization , quadrature (astronomy) , crank–nicolson method , mathematical analysis , norm (philosophy) , galerkin method , boundary value problem , rate of convergence , nonlinear system , finite element method , quantum mechanics , physics , channel (broadcasting) , political science , law , electrical engineering , thermodynamics , engineering

We propose and analyze an application of a fully discrete C 2 spline quadrature Petrov‐Galerkin method for spatial discretization of semi‐linear parabolic initial‐boundary value problems on rectangular domains. We prove second order in time and optimal order H 1 norm convergence in space for the extrapolated Crank‐Nicolson quadrature Petrov‐Galerkin scheme. We demonstrate numerically both L 2 and H 1 norm optimal order convergence of the scheme even if the nonlinear source term is not smooth. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005.

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