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• W3113292938 abstract "A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are $mathcal{L}mathcal{L}^*$ methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h-refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order $p > 1$ when the exact solution is a constant function. We show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions." @default.
• W3113292938 created "2020-12-21" @default.
• W3113292938 creator A5018678142 @default.
• W3113292938 date "2020-12-17" @default.
• W3113292938 modified "2023-09-27" @default.
• W3113292938 title "A priori error analysis of high-order LL* (FOSLL*) finite element methods." @default.
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• W3113292938 hasPublicationYear "2020" @default.
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