an rp-adaptive finite element discretization applied to physically non ...
an rp-adaptive finite element discretization applied to physically non ...
an rp-adaptive finite element discretization applied to physically non ...
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1e+02PSfrag replacementsxyzVera Nübel, Alex<strong>an</strong>der Düster <strong>an</strong>d Ernst R<strong>an</strong>krira1e+021e+011e+00PSfrag replacementsrelative error η [%]1e+011e+001e-011e-021e-031e-04interface mesh, 6 <strong>element</strong>suniform h-version, p=2<strong>adaptive</strong> <strong>rp</strong>-version1e+021e+011e+001e-011e-021e-031e-041e-051e+001e+011e+021e+031e+041e+051e+06relative error η [%]degrees of freedom Ninterface mesh, 6 <strong>element</strong>suniform h-version, p=2<strong>adaptive</strong> <strong>rp</strong>-versionyzr ir ax1e-051e+01 1e+02 1e+03 1e+04 1e+05 1e+06degrees of freedom N√|Uref −UFigure 4: Relative error η =F E|∫U ref100 [%] with U = 1 2 Ω εT σ dΩ for 3D-problemAcknowledgementThis study has been sponsored with the help of a gr<strong>an</strong>t from the Deutsche Forschungsgemeinschaft(DFG, RA 624/6-3, RA 624/6-4). This support is gratefully acknowledged.REFERENCES[1] A. Düster <strong>an</strong>d E. R<strong>an</strong>k. The p-version of the <strong>finite</strong> <strong>element</strong> method compared <strong>to</strong><strong>an</strong> <strong>adaptive</strong> h-version for the deformation theory of plasticity, Computer Methods inApplied Mech<strong>an</strong>ics <strong>an</strong>d Engineering, 190, 1925-1935, 2001.[2] E. Stein. Error-Controlled Adaptive Finite Elements in Solid Mech<strong>an</strong>ics, John Wiley& Sons, 2002.[3] B. Szabó, A. Düster <strong>an</strong>d E. R<strong>an</strong>k. The p-version of the <strong>finite</strong> <strong>element</strong> method, In:Encyclopedia of Computational Mech<strong>an</strong>ics, E. Stein, R. de Borst <strong>an</strong>d T. Hughes,edi<strong>to</strong>rs, John Wiley & Sons, 2004.[4] V. Nübel, A. Düster <strong>an</strong>d E. R<strong>an</strong>k. An <strong>rp</strong>-<strong>adaptive</strong> <strong>finite</strong> <strong>element</strong> method for thedeformation theory of plasticity, submitted <strong>to</strong>: Computational Mech<strong>an</strong>ics, 2004.4
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