Two classes of mixed finite element methods
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Error analysis of some Galerkin least squares methods for the elasticity equations
SIAM Journal on Numerical Analysis
A posteriori error estimation and adaptive mesh-refinement techniques
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
A posteriori error estimate for the mixed finite element method
Mathematics of Computation
An a posteriori error estimate for a first-kind integral equation
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
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In this paper, we provide a priori and a posteriori error analyses of an augmented mixed finite element method with Lagrange multipliers applied to elliptic equations in divergence form with mixed boundary conditions. The augmented scheme is obtained by including the Galerkin least-squares terms arising from the constitutive and equilibrium equations. We use the classical Babuska-Brezzi theory to show that the resulting dual-mixed variational formulation and its Galerkin scheme defined with Raviart-Thomas spaces are well posed, and also to derive the corresponding a priori error estimates and rates of convergence. Then, we develop a reliable and efficient residual-based a posteriori error estimate and a reliable and quasi-efficient Ritz projection-based one, as well. Finally, several numerical results illustrating the performance of the augmented scheme and the associated adaptive algorithms are reported.