A posteriori error estimates for the Stokes equations: a comparison
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A posteriori error estimates based on hierarchical bases
SIAM Journal on Numerical Analysis
Finite Elements in Analysis and Design
First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Least-squares mixed finite elements for second-order elliptic problems
SIAM Journal on Numerical Analysis
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
SIAM Journal on Numerical Analysis
A least-squares approach based on a discrete minus one inner product for first order systems
Mathematics of Computation
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
Computational Differential Equations
Computational Differential Equations
SIAM Journal on Numerical Analysis
An Adaptive Least-Squares Mixed Finite Element Method for Elasto-Plasticity
SIAM Journal on Numerical Analysis
A posteriori error estimators for the first-order least-squares finite element method
Journal of Computational and Applied Mathematics
Sharp $L_2$-Norm Error Estimates for First-Order div Least-Squares Methods
SIAM Journal on Numerical Analysis
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We propose a goal-oriented, local a posteriori error estimator for H(div) least-squares (LS) finite element methods. Our main interest is to develop an a posteriori error estimator for the flux approximation in a preassigned region of interest $D \subset \Omega$. The estimator is obtained from the LS functional by scaling residuals with proper weight coefficients. The weight coefficients are given in terms of local mesh size $h_T$ and a function $\omega_D$ depending on the distance to $D$. This new error estimator measures the pollution effect from the outside region of $D$ and provides a basis for local refinement in order to efficiently approximate the solution in $D$. Numerical experiments show superior performances of our goal-oriented a posteriori estimators over the standard LS functional and global error estimators.