Some a posteriori error estimators for elliptic partial differential equations

Authors:
R. E. Bank and A. Weiser

Journal:
Math. Comp. **44** (1985), 283-301

MSC:
Primary 65N30; Secondary 65N15

DOI:
https://doi.org/10.1090/S0025-5718-1985-0777265-X

MathSciNet review:
777265

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Abstract: We present three new a posteriori error estimators in the energy norm for finite element solutions to elliptic partial differential equations. The estimators are based on solving local Neumann problems in each element. The estimators differ in how they enforce consistency of the Neumann problems. We prove that as the mesh size decreases, under suitable assumptions, two of the error estimators approach upper bounds on the norm of the true error, and all three error estimators are within multiplicative constants of the norm of the true error. We present numerical results in which one of the error estimators appears to converge to the norm of the true error.

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0777265-X

Article copyright:
© Copyright 1985
American Mathematical Society