This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Barrenechea, Gabriel R.John, VolkerKnobloch, Petr2016-03-242019-06-2820120946-8633https://doi.org/10.34657/1834https://oa.tib.eu/renate/handle/123456789/1784An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.application/pdfeng510Finite element methodlocal projection stabilizationcrosswind diffusionconvection-diffusion-reaction equationwell posednesstime dependent problemstabilityerror estimatesReport