SIAM Journal on Numerical Analysis
A posteriori error estimates for nonconforming approximations of Steklov eigenvalue problems
Computers & Mathematics with Applications
Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization
SIAM Journal on Optimization
Function Value Recovery and Its Application in Eigenvalue Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
An Adaptive P1 Finite Element Method for Two-Dimensional Maxwell's Equations
Journal of Scientific Computing
Computers & Mathematics with Applications
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Residual-based a posteriori error estimates are derived within a unified setting for lowest-order conforming, nonconforming, and mixed finite element schemes. The various residuals are identified for all techniques and problems as the operator norm ||ℓ|| of a linear functional of the form**in the variable υ of a Sobolev space V. The main assumption is that the first-order finite element space ** is included in the kernel Ker ℓ of ℓ. As a consequence, any residual estimator that is a computable bound of ||ℓ|| can be used within the proposed frame without further analysis for nonconforming or mixed FE schemes. Applications are given for the Laplace, Stokes, and Navier-Lamè equations.