A new family of mixed finite elements in IR3
Numerische Mathematik
Mixed finite elements for second order elliptic problems in three variables
Numerische Mathematik
A local post-processing technique for improving the accuracy in mixed finite-element approximations
SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A posteriori error estimation and adaptive mesh-refinement techniques
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Convergence of Adaptive Discontinuous Galerkin Approximations of Second-Order Elliptic Problems
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
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We present the first a posteriori error analysis of the so-called hybridizable discontinuous Galerkin (HDG) methods for second-order elliptic problems. We show that the error in the flux can be controlled by only two terms. The first term captures the so-called data oscillation. The second solely depends on the difference between the trace of the scalar approximation and the corresponding numerical trace. Numerical experiments verifying the reliability and efficiency of the estimate in two-space dimensions are presented.