Mathematics of Computation
Two-grid Discretization Techniques for Linear and Nonlinear PDEs
SIAM Journal on Numerical Analysis
Element analysis method and superconvergence
Finite element methods
A survey of superconvergence techniques in finite element methods
Finite element methods
An adaptive strategy for elliptic problems including a posteriori controlled boundary approximation
Mathematics of Computation
Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
SIAM Journal on Numerical Analysis
Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
SIAM Journal on Numerical Analysis
Two-grid finite volume element method for linear and nonlinear elliptic problems
Numerische Mathematik
Discontinuous Galerkin Methods for Quasi-Linear Elliptic Problems of Nonmonotone Type
SIAM Journal on Numerical Analysis
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In this paper, we are concerned with the linear finite element approximations to the second-order quasi-linear elliptic problems. By means of an interpolation postprocessing technique, we develop the global superconvergence estimates in the H^1- and W^1^,^~-norms provided the weak solutions are sufficiently smooth. Based on the global superconvergent approximations, we introduce and analyze the efficient postprocessing-based a posteriori error estimators, measured by the H^1- and W^1^,^~-norms respectively. These can be used to assess the accuracy of the finite element solutions in applications. Numerical experiments are given to illustrate the global superconvergence estimates and the performance of the proposed estimators.