000190432 001__ 190432
000190432 005__ 20181203023325.0
000190432 0247_ $$2doi$$a10.1016/S0045-7825(98)00361-2
000190432 022__ $$a0045-7825
000190432 02470 $$2ISI$$a000081650700008
000190432 037__ $$aARTICLE
000190432 245__ $$aStable spectral methods for conservation laws on triangles with unstructured grids
000190432 260__ $$bELSEVIER SCIENCE SA$$c1999
000190432 269__ $$a1999
000190432 336__ $$aJournal Articles
000190432 520__ $$aThis paper presents an asymptotically stable scheme for the spectral approximation of linear conservation laws defined on a triangle. Lagrange interpolation on a general two-dimensional nodal set is employed and, by imposing the boundary conditions weakly through a penalty term, the scheme is proven stable in L-2. This result is established for a general unstructured grid in the triangle. A special case, for which the nodes along the edges of the triangle are chosen as the Legendre Gauss-Lobatto quadrature points, is discussed in detail. The eigenvalue spectrum of the approximation to the advective operator is computed and is shown to result in an O(n(-2)) restriction on the time-step when considering explicit time-stepping. (C) 1999 Elsevier Science S.A. All rights reserved.
000190432 700__ $$0247428$$g232231$$aHesthaven, Jan S.
000190432 700__ $$aGottlieb, D
000190432 773__ $$j175$$tComputer Methods in Applied Mechanics and Engineering$$k3-4$$q361-381
000190432 909C0 $$xU12703$$0252492$$pMCSS
000190432 909CO $$pSB$$particle$$ooai:infoscience.tind.io:190432
000190432 937__ $$aEPFL-ARTICLE-190432
000190432 970__ $$aHesthaven1999c/MCSS
000190432 973__ $$rREVIEWED$$sPUBLISHED$$aOTHER
000190432 980__ $$aARTICLE