000190655 001__ 190655
000190655 005__ 20190316235746.0
000190655 0247_ $$2doi$$a10.1016/j.jcp.2013.09.041
000190655 022__ $$a0021-9991
000190655 037__ $$aARTICLE
000190655 245__ $$aStable multi-domain spectral penalty methods for fractional partial differential equations
000190655 269__ $$a2014
000190655 260__ $$bElsevier$$c2014
000190655 336__ $$aJournal Articles
000190655 520__ $$aWe propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.
000190655 6531_ $$aFractional partial differential equation
000190655 6531_ $$aFractional differential matrix
000190655 6531_ $$aMulti-domain spectral method
000190655 6531_ $$aPenalty method
000190655 700__ $$aXu, Qinwu
000190655 700__ $$0247428$$g232231$$aHesthaven, Jan S.
000190655 773__ $$j257$$tJournal of Computational Physics$$q241-258
000190655 8564_ $$uhttp://www.sciencedirect.com/science/article/pii/S0021999113006554$$zURL
000190655 8564_ $$uhttps://infoscience.epfl.ch/record/190655/files/JCP2014.pdf$$zPreprint$$s427509$$yPreprint
000190655 909C0 $$xU12703$$0252492$$pMCSS
000190655 909CO $$ooai:infoscience.tind.io:190655$$qGLOBAL_SET$$pSB$$particle
000190655 917Z8 $$x232231
000190655 917Z8 $$x232231
000190655 937__ $$aEPFL-ARTICLE-190655
000190655 973__ $$rREVIEWED$$sPUBLISHED$$aOTHER
000190655 980__ $$aARTICLE