From 6b1419143494456b3a8092f227ec4436c2e28872 Mon Sep 17 00:00:00 2001 From: Daniel Shapero Date: Wed, 15 May 2024 21:24:42 -0700 Subject: [PATCH] Add some references These papers show that Q(k) x Q(k - 1) is LBB-stable but that its stability constant degrades with aspect ratio, hence superiority of Q(k) * Q(k -2) whose stability constant only degrades with k. --- tensor-product-stokes.bib | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) diff --git a/tensor-product-stokes.bib b/tensor-product-stokes.bib index bc4de51..6c4396a 100644 --- a/tensor-product-stokes.bib +++ b/tensor-product-stokes.bib @@ -132,3 +132,26 @@ @article{isaac2015solution year={2015}, publisher={SIAM} } + + +@article{ainsworth2000stability, + title={The stability of mixed hp-finite element methods for {Stokes} flow on high aspect ratio elements}, + author={Ainsworth, Mark and Coggins, Patrick}, + journal={SIAM Journal on Numerical Analysis}, + volume={38}, + number={5}, + pages={1721--1761}, + year={2000}, + publisher={SIAM} +} + + +@article{toselli2003mixed, + title={Mixed hp-finite element approximations on geometric edge and boundary layer meshes in three dimensions}, + author={Toselli, Andrea and Schwab, Christoph}, + journal={Numerische Mathematik}, + volume={94}, + pages={771--801}, + year={2003}, + publisher={Springer} +}