Adaptive mixed FEM combined with the method of characteristics for stationary convection–diffusion–reaction problems

Antony Oliver, Mary Chriselda; González Taboada, María

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http://hdl.handle.net/2183/37706

Adaptive mixed FEM combined with the method of characteristics for stationary convection–diffusion–reaction problems

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Gonzalez_Maria_2023_Adaptive_mixed_FEM_combined_with_the_method_of_characteristics_for_stationary_convection_diffusion_reaction_problems.pdf (6.62 MB)

Identifiers

URI: http://hdl.handle.net/2183/37706

DOI: 10.1016/j.finel.2023.104045

Publication date

2023-12-01

Authors

Antony Oliver, Mary Chriselda

González Taboada, María

Bibliographic citation

M. C. Antony Oliver, and M. González, "Adaptive mixed FEM combined with the method of characteristics for stationary convection–diffusion–reaction problems", Finite Elements in Analysis and Design, Vol. 227, 1 December 2023, 104045, doi: 10.1016/j.finel.2023.104045

Abstract

[Abstract]: We consider a stationary convection–diffusion–reaction model problem in a two- or three-dimensional bounded domain. We approximate this model by a non-stationary problem and propose a numerical method that combines the method of characteristics with an augmented mixed finite element procedure. We show that this scheme has a unique solution. We also derive a residual-based a posteriori error indicator and prove it is reliable and locally efficient. Finally, we provide some numerical experiments that illustrate the performance of the adaptive algorithm.