A parameter-free dynamic diffusion method for advection–diffusion–reaction problems
In this paper, we present a two-scale finite element formulation, named Dynamic Diffusion (DD), for advection–diffusion–reaction problems. By decomposing the velocity field in coarse and subgrid scales, the latter is used to determine the smallest amount of artificial diffusion to minimize the coars...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) 2018-01, Vol.75 (1), p.307-321 |
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| container_title | Computers & mathematics with applications (1987) |
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| creator | Valli, Andrea M.P. Almeida, Regina C. Santos, Isaac P. Catabriga, Lucia Malta, Sandra M.C. Coutinho, Alvaro L.G.A. |
| description | In this paper, we present a two-scale finite element formulation, named Dynamic Diffusion (DD), for advection–diffusion–reaction problems. By decomposing the velocity field in coarse and subgrid scales, the latter is used to determine the smallest amount of artificial diffusion to minimize the coarse-scale kinetic energy. This is done locally and dynamically, by imposing some constraints on the resolved scale solution, yielding a parameter-free consistent method. The subgrid scale space is defined by using bubble functions, whose degrees of freedom are locally eliminated in favor of the degrees of freedom that live on the resolved scales. Convergence tests on a two-dimensional example are reported, yielding optimal rates. In addition, numerical experiments show that DD method is robust for a wide scope of application problems. |
| doi_str_mv | 10.1016/j.camwa.2017.09.020 |
| format | Article |
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| ispartof | Computers & mathematics with applications (1987), 2018-01, Vol.75 (1), p.307-321 |
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| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present) |
| subjects | Advection Advection–diffusion–reaction equations Bubble functions Bubbles Decomposition reactions Degrees of freedom Diffusion Dynamic Diffusion method Energy conservation Finite element analysis Finite element method Kinetic energy Multiscale finite element formulation Parameters Robustness (mathematics) Velocity distribution |
| title | A parameter-free dynamic diffusion method for advection–diffusion–reaction problems |
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