Projection methods with different trial and test spaces

Author:
M. S. Mock

Journal:
Math. Comp. **30** (1976), 400-416

MSC:
Primary 65N30

DOI:
https://doi.org/10.1090/S0025-5718-1976-0423840-6

MathSciNet review:
0423840

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Abstract: We consider finite element projection methods for linear partial differential equations, in which the spaces of trial functions and test functions may be different. In addition to approximation and smoothness properties, conditions implying equality of dimensions and uniform coerciveness are required, the most important of which resembles a strong form of an inverse assumption.

Our results provide a mechanism for the difference in the rate of convergence of Galerkin procedures with cubic splines and Hermite cubics, applied to first order symmetric hyperbolic problems [13].

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DOI:
https://doi.org/10.1090/S0025-5718-1976-0423840-6

Article copyright:
© Copyright 1976
American Mathematical Society