Artículo
Error estimates of a linear decoupled Euler–FEM scheme for a mass diffusion model
Autor/es | Guillén González, Francisco Manuel
Gutiérrez Santacreu, Juan Vicente |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2011 |
Fecha de depósito | 2019-10-17 |
Publicado en |
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Resumen | We present error estimates of a linear fully discrete scheme for a threedimensional
mass diffusion model for incompressible fluids (also called Kazhikhov–
Smagulov model). All unknowns of the model (velocity, pressure ... We present error estimates of a linear fully discrete scheme for a threedimensional mass diffusion model for incompressible fluids (also called Kazhikhov– Smagulov model). All unknowns of the model (velocity, pressure and density) are approximated in space by C0-finite elements and in time an Euler type scheme is used decoupling the density from the velocity–pressure pair. If we assume that the velocity and pressure finite-element spaces satisfy the inf–sup condition and the density finite-element space contains the products of any two discrete veloci-ties, we first obtain point-wise stability estimates for the density, under the constraint lim(h,k)→0 h/k = 0 (h and k being the space and time discrete parameters, respectively), and error estimates for the velocity and density in energy type norms, at the same time. Afterwards, error estimates for the density in stronger norms are deduced. All these error estimates will be optimal (of order O(h + k)) for regular enough solu-tions without imposing nonlocal compatibility conditions at the initial time. Finally, we also study two convergent iterative methods for the two problems to solve at each time step, which hold constant matrices (independent of iterations). |
Identificador del proyecto | MTM2006-07932
P06-FQM-02373 |
Cita | Guillén González, F.M. y Gutiérrez Santacreu, J.V. (2011). Error estimates of a linear decoupled Euler–FEM scheme for a mass diffusion model. Numerische Mathematik, 117 (2), 333-371. |
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