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Convergence of the interpolated coefficient finite element method for the two‐dimensional elliptic sine‐Gordon equations
Author(s) -
Wang Cheng
Publication year - 2011
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.20526
Subject(s) - mathematics , discretization , mathematical analysis , finite element method , partial differential equation , subsequence , dirichlet boundary condition , rate of convergence , convergence (economics) , norm (philosophy) , elliptic partial differential equation , boundary value problem , channel (broadcasting) , electrical engineering , engineering , physics , economic growth , political science , law , economics , thermodynamics , bounded function
An interpolated coefficient finite element method is presented and analyzed for the two‐dimensional elliptic sine‐Gordon equations with Dirichlet boundary conditions. It is proved that the discretization scheme admits at least one solution, and that a subsequence of the approximation solutions converges to an exact solution in L 2 ‐norm as the mesh size tends to zero. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011