On the stability and convergence of higher-order mixed finite element methods for second-order elliptic problems

Author:
Manil Suri

Journal:
Math. Comp. **54** (1990), 1-19

MSC:
Primary 65N30; Secondary 65N10

DOI:
https://doi.org/10.1090/S0025-5718-1990-0990603-X

MathSciNet review:
990603

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Abstract: We investigate the use of higher-order mixed methods for second-order elliptic problems by establishing refined stability and convergence estimates which take into account both the mesh size *h* and polynomial degree *p*. Our estimates yield asymptotic convergence rates for the *p*- and *h -- p*-versions of the finite element method. They also describe more accurately than previously proved estimates the increased rate of convergence expected when the *h*-version is used with higher-order polynomials. For our analysis, we choose the Raviart-Thomas and the Brezzi-Douglas-Marini elements and establish optimal rates of convergence in both *h* and *p* (up to arbitrary ).

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DOI:
https://doi.org/10.1090/S0025-5718-1990-0990603-X

Article copyright:
© Copyright 1990
American Mathematical Society