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<https://discovery.ucl.ac.uk/id/eprint/1384765> <http://purl.org/dc/terms/title> "Stabilized Galerkin approximation of convection-diffusion-reaction equations: Discrete maximum principle and convergence"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/1384765> <http://purl.org/ontology/bibo/abstract> "We analyze a nonlinear shock-capturing scheme for H1-conform-ing, piecewise-affine finite element approximations of linear elliptic problems. The meshes are assumed to satisfy two standard conditions: a local quasi-uniformity property and the Xu-Zikatanov condition ensuring that the stiffness matrix associated with the Poisson equation is an M-matrix. A discrete maximum principle is rigorously established in any space dimension for convection-diffusion-reaction problems. We prove that the shock-capturing finite element solution converges to that without shock-capturing if the cell Péclet numbers are sufficiently small. Moreover, in the diffusion-dominated regime, the difference between the two finite element solutions super-converges with respect to the actual approximation error. Numerical experiments on test problems with stiff layers confirm the sharpness of the a priori error estimates."^^<http://www.w3.org/2001/XMLSchema#string> .
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