A finite element method for second order nonvariational elliptic problems

Omar Lakkis, Tristan Pryer

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We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of a 'finite element Hessian' and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasilinear PDE, all in nonvariational form.
Original languageEnglish
Pages (from-to)786-801
Number of pages16
JournalSIAM Journal on Scientific Computing
Issue number2
Early online date5 Apr 2011
Publication statusPublished - 2011


  • math.NA
  • 65N30, 65Y20, 65F99


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