A theory for local, posteriori, pointwise, residual-based estimation of the finite element error

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

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A procedure for a posteriori error estimation for \(h\)-\(p\) finite element methods
Asymptotically exact a posteriori error estimator for biquadratic elements
A posteriori error estimators for second order elliptic systems. I: Theoretical foundations and a posteriori error analysis
A posteriori error estimators for second order elliptic systems. II: An optimal order process for calculating self-equilibrating fluxes
A unified approach to a posteriori error estimation using element residual methods
An asymptotically exact, pointwise, a posteriori error estimator for linear, elliptic, one-dimensional problems with possible singularities in the solution
The equilibrium method for local, a posteriori, pointwise estimation of the finite element error
Guaranteed computable bounds for the exact error in the finite element solution. I: One-dimensional model problem
Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
The post-processing approach in the finite element method—Part 3:A posteriori error estimates and adaptive mesh selection
The self-equilibration of residuals and complementarya posteriori error estimates in the finite element method
Error Estimate Procedure in the Finite Element Method and Applications
A model study of element residual estimators for linear elliptic problems: The quality of the estimators in the interior of meshes of triangles and quadrilaterals
Guaranteed computable bounds for the exact error in the finite element solution?Part II: bounds for the energy norm of the error in two dimensions
Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace's, Poisson's, and the elasticity equations

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