We give an elementary derivation of an extension of the Ritz method to trial functions that do not satisfy essential boundary conditions. As in the Babuška-Brezzi approach boundary conditions are treated as variational constraints and Lagrange multipliers are used to remove them. However, we avoid the saddle point reformulation of the problem and therefore do not have to deal with the Babuška-Brezzi inf-sup condition. In higher dimensions boundary weights are used to approximate the boundary conditions, and the assumptions in our convergence proof are stated in terms of completeness of the trial functions and of the boundary weights. These assumptions are much more straightforward to verify than the Babuška-Brezzi condition. We also discuss limitations of the method and implementation issues that follow from our analysis and examine a number of examples, both analytic and numerical.
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from #AlexandrosSfakianakis via Alexandros G.Sfakianakis on Inoreader http://ift.tt/2jCvX3K via IFTTT
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Abstract Purpose of Review Our goal is to summarize the airway disease literature since September 11, 2001 (9/11), focusing on studies pub...
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Vol.25 No.2 from #AlexandrosSfakianakis via Alexandros G.Sfakianakis on Inoreader http://ift.tt/1P7bHxT via IFTTT
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Publication date: Available online 16 January 2017 Source: International Journal of Pediatric Otorhinolaryngology Author(s): Kaveh Karimn...
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