G. W. Zumbusch.
Simultanous h-p Adaptation in Multilevel Finite Elements.
Dissertation, Fachbereich Mathematik und Informatik, FU Berlin, 1995.
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An important tool in engineering is the finite element method.... The combination of both methods, the h-p version, supplies the pre-asymptotic exponentially convergent p-version continuously with properly adapted grids. Hence it achieves the superior exponential convergence asymptotically, too, instead of algebraic convergence of its ingredients the h-version and the p-version. Although the first theoretical results claiming these convergence rates are quite classic, the number of codes using the h-p-version of finite elements is still rather limited. Reasons for that are the pure implementational complexity and the details, in conjunction with the rumor of engineers' low precision requirements. But the major reason is the lack of a robust (self-) adaptive control delivering the desired exponential convergence. ...