Asymptotic error expansion and richardson extrapolation for linear fine elements
Numerische Mathematik
A two-grid discretization scheme for eigenvalue problems
Mathematics of Computation
Two-Sided Arnoldi and Nonsymmetric Lanczos Algorithms
SIAM Journal on Matrix Analysis and Applications
Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
SIAM Journal on Numerical Analysis
A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
SIAM Journal on Numerical Analysis
A New Finite Element Gradient Recovery Method: Superconvergence Property
SIAM Journal on Scientific Computing
A unifying theory of a posteriori finite element error control
Numerische Mathematik
Enhancing Eigenvalue Approximation by Gradient Recovery
SIAM Journal on Scientific Computing
Function, Gradient, and Hessian Recovery Using Quadratic Edge-Bump Functions
SIAM Journal on Numerical Analysis
Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?
SIAM Journal on Numerical Analysis
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Function value recovery techniques for linear finite elements are discussed. Using the recovered function and its gradient, we are able to enhance the eigenvalue approximation and increase its convergence rate to $h^{2\alpha}$, where $\alpha 1$ is the superconvergence rate of the recovered gradient. This is true in both symmetric and nonsymmetric eigenvalue problems.