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  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  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  were based.
|Number of pages||15|
|Journal||Computer Methods in Applied Mechanics and Engineering|
|Publication status||Published - 1997|