Author： Barrios Tomás P.
Publisher： Taylor & Francis Ltd
ISSN： 0163-0563
Source： Numerical Functional Analysis and Optimization, Vol.28, Iss.3-4, 2007-03, pp. : 265-286
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Abstract
We use Galerkin least-squares terms and biorthogonal wavelet bases to develop a new stabilized dual-mixed finite element method for second-order elliptic equations in divergence form with Neumann boundary conditions. The approach introduces the trace of the solution on the boundary as a new unknown that acts also as a Lagrange multiplier. We show that the resulting stabilized dual-mixed variational formulation and the associated discrete scheme defined with Raviart-Thomas spaces are well-posed and derive the usual a priori error estimates and the corresponding rate of convergence. Furthermore, a reliable and efficient residual-based a posteriori error estimator and a reliable and quasi-efficient one are provided.
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