Title:
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Stabilized FIF/FEM formulation for multidimensional advection-diffusion-reaction problems
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Author:
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Oñate Ibáñez de Navarra, Eugenio; Miquel Canet, Juan; Zárate Araiza, José Francisco
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Other authors:
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Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. GMNE - Grup de Mètodes Numèrics en Enginyeria; Universitat Politècnica de Catalunya. RMEE - Grup de Resistència de Materials i Estructures en l'Enginyeria |
Abstract:
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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. |
Subject(s):
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-Difference equations--Numerical solutions -Research Report CIMNE -Equacions diferencials--solucions numèriques -Classificació AMS::65 Numerical analysis::65L Ordinary differential equations |
Rights:
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Document type:
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Article - Draft Report |
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