On boundary-hybrid finite element methods for the Laplace equation

J.M.L. Maubach, P.J. Rabier

    Research output: Contribution to journalArticleAcademicpeer-review

    Abstract

    About two decades ago, I. Babu ka, J.T. Oden and J.K. Lee introduced finite element methods that calculate the normal derivative of the solution along the mesh interfaces and recover the solution via local Neumann problems. These methods for the treatment of the homogeneous Laplace equation were called ‘boundary-hybrid methods’. The approach was revisited in [12] for general symmetric and positive definite elliptic equations with homogeneous boundary conditions. The new approximation is nonconforming and lends itself well for an a posteriori error estimator for conforming finite element approximations. Numerical tests presented in [12] corroborated that the error estimates are accurate and cheap for conforming approximations. This paper provides the iterative solution methods and Galerkin discretization methods on which the numerical approximations in [12] were based.
    Original languageEnglish
    Pages (from-to)273-287
    Number of pages15
    JournalComputer Methods in Applied Mechanics and Engineering
    Volume150
    Issue number1-4
    DOIs
    Publication statusPublished - 1997

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