Summary
We investigate stabilized Galerkin approximations of certain steady and unsteady convection-diffusion problems with linear and nonlinear source terms. We derive nonlinear stream line and cross wind diffusion methods that guarantee a discrete maximum principle. Our theoretical results apply to finite element methods with piecewise constant, discontinuous approximation in time and piecewise linear, continuous approximation in space on strictly acute triangulations. Practical implementations of the present methods are compared to previous schemes which lacked theoretical justification. Numerical results for various model problems are discussed in terms of solution quality and computational costs.
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References
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© 2003 Springer-Verlag Italia
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Burman, E., Ern, A. (2003). The discrete maximum principle for stabilized finite element methods. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_52
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DOI: https://doi.org/10.1007/978-88-470-2089-4_52
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2167-9
Online ISBN: 978-88-470-2089-4
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