Onate 2003a - Revision history

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Cinmemj at 13:50, 16 November 2018

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Cinmemj at 13:49, 16 November 2018

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Cinmemj at 15:23, 13 November 2018

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Cinmemj at 11:36, 31 October 2018

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Cinmemj: Created page with "

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-<!-- metadata commented in wiki content
+Published in ''Comput. Meth. Appl. Mech. Engng.'', Vol. 192 (28-30), pp. 3043-3059, 2003<br />
-==MULTISCALE COMPUTATIONAL ANALYSIS IN MECHANICS USING FINITE CALCULUS. AN INTRODUCTION==
+doi: 10.1016/S0045-7825(03)00340-2
 ==Abstract==

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_937954379-majesus2.png|240px|Equilibrium of fluxes in a  space balance domain of finite size]]
+|[[Image:Draft_Samper_937954379-majesus2.png|440px|Equilibrium of fluxes in a  space balance domain of finite size]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 5:''' Equilibrium of fluxes in a  space balance domain of finite size
 |}
 Let us express now the fluxes <math display="inline">q_A</math> and <math display="inline">q_B</math> in terms of the flux at an arbitrary point <math display="inline">C</math> within the balance domain (Figure A.1). Expanding <math display="inline">q_A</math> and <math display="inline">q_B</math> in Taylor series around point <math display="inline">C</math> up to second order terms gives

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_937954379-Fig2.png|600px|1D advection-diffusion problem solved with two linear elements (γ=50). Unstable solution (- - -) obtained for α=0 (Galerkin). Stabilized solution (&#8211;-) obtained with the FIC method for α= (1+ 10⁻¹⁰)(1- 1\over γ)]]
+|[[Image:Draft_Samper_937954379-Fig2.png|400px|1D advection-diffusion problem solved with two linear elements (γ=50). Unstable solution (- - -) obtained for α=0 (Galerkin). Stabilized solution (&#8211;-) obtained with the FIC method for α= (1+ 10⁻¹⁰)(1- 1\over γ)]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 2:''' 1D advection-diffusion problem solved with two linear elements (<math>\gamma =50</math>). Unstable solution (- - -) obtained for <math>\alpha =0</math> (Galerkin). Stabilized solution (&#8211;-) obtained with the FIC method for <math>\alpha = (1+ 10^{-10})(1- {1\over \gamma })</math>
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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_937954379-Fig3.png|600px|1D advection-diffusion problem solved with two linear elements. Initial stabilized FIC solution (curve A). Enhanced solutions over element 2&#8211;3 using a hierarchical trigonometric interpolation (curve B) and an exponential interpolation (curve C)]]
+|[[Image:Draft_Samper_937954379-Fig3.png|400px|1D advection-diffusion problem solved with two linear elements. Initial stabilized FIC solution (curve A). Enhanced solutions over element 2&#8211;3 using a hierarchical trigonometric interpolation (curve B) and an exponential interpolation (curve C)]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 3:''' 1D advection-diffusion problem solved with two linear elements. Initial stabilized FIC solution (curve A). Enhanced solutions over element 2&#8211;3 using a hierarchical trigonometric interpolation (curve B) and an exponential interpolation (curve C)

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 The same ideas can be used to solve a wide class of multiscale problems in mechanics where the solution changes in several orders of magnitude in specific regions.
-===BIBLIOGRAPHY===
+==REFERENCES==
 <div id="cite-1"></div>

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