000102929 001__ 102929
000102929 005__ 20181203020804.0
000102929 0247_ $$2doi$$a10.1016/S0045-7825(02)00318-3
000102929 02470 $$2DAR$$a332
000102929 02470 $$2ISI$$a000177032300003
000102929 037__ $$aARTICLE
000102929 245__ $$aNonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation
000102929 269__ $$a2002
000102929 260__ $$c2002
000102929 336__ $$aJournal Articles
000102929 520__ $$aWe investigate stabilized Galerkin approximations of linear and nonlinear convection-diffusion-reaction equations. We derive nonlinear streamline and cross-wind diffusion methods that guarantee a discrete maximum principle for strictly acute meshes and first order polynomial interpolation. For pure convection-diffusion problems, the discrete maximum principle is achieved using a nonlinear cross-wind diffusion factor that depends on the angle between the discrete solution and the flow velocity. For convection-diffusion-reaction problems, two methods are considered: residual based, isotropic diffusion and the previous nonlinear cross-wind diffusion factor supplemented by additional isotropic diffusion scaling as the square of the mesh size. Practical versions of the present methods suitable for numerical implementation are compared to previous discontinuity capturing schemes lacking theoretical justification. Numerical results are investigated in terms of both solution quality (violation of maximum principle, smearing of internal layers) and computational costs
000102929 6531_ $$achemically reactive flow combustion computational fluid dynamics convection 	finite element analysis Galerkin method maximum principle reaction-diffusion 	systems
000102929 700__ $$0240436$$aBurman, Erik$$g138272
000102929 700__ $$aErn, Alexandre
000102929 773__ $$j191$$k35$$q3833-55$$tComputer Methods in Applied Mechanics and Engineering
000102929 909C0 $$0252102$$pCMCS$$xU10797
000102929 909CO $$ooai:infoscience.tind.io:102929$$pSB$$particle
000102929 937__ $$aCMCS-ARTICLE-2002-002
000102929 970__ $$aBurman2002/CMCS
000102929 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000102929 980__ $$aARTICLE