Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Dg And Hdg Methods For Curved Structures, Li Fan
Dg And Hdg Methods For Curved Structures, Li Fan
Wayne State University Dissertations
We introduce and analyze discontinuous Galerkin methods
for a Naghdi type arch model. We prove that, when the numerical traces are properly chosen, the methods display optimal convergence uniformly with respect to the thickness of the arch. These methods are thus free from membrane and shear locking.
We also prove that, when polynomials of degree $k$ are used,
{\em all} the numerical traces superconverge with a rate of order
h 2k+1.
Based on the superconvergent phenomenon and we show how to
post-process them in an element-by-element fashion
to obtain a far better approximation. Indeed, we prove that,
if polynomials …