Stabilized FIF/FEM formulation for multidimensional advection-diffusion-reaction problems
A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. For 1D problems the stabilization te...
| Autores: | , , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/171048 |
| Acceso en línea: | https://hdl.handle.net/2117/171048 |
| Access Level: | acceso abierto |
| Palabra clave: | Difference equations--Numerical solutions Research Report CIMNE Equacions diferencials--solucions numèriques Classificació AMS::65 Numerical analysis::65L Ordinary differential equations |
| Sumario: | A stabilized finite element method (FEM) for the multidimensional steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. For 1D problems the stabilization terms act as a nonlinear additional diffusion governed by a single stabilization parameter. It is shown that for multidimensional problems an orthotropic stabilizing diffusion must be added along the principal directions of curvature of the solution. A simple iterative algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. Numerical results for 1D and 2D problems with sharp gradients are presented showing the effectiveness and accuracy of the new stabilized formulation. |
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