CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="120"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'non-interactive',cRay: '91348a0e3c0ffce3',cH: 'jrqllzYi18EcevNRQ..HvoaWDeonsWYbk8Ips.Iuc2k-1739782325-1.2.1.1-EXCERZqI4FzS.bsSzsW0gTPX.fz3ThvSsKb2.gcTYUZCLguA5PplslHlnacLKtYj',cUPMDTk: "\/search?q=finite%20element%20method&__cf_chl_tk=8snPJkpV02WwymthlRs6sg1Th5dCHWe394dSJUYKqg0-1739782325-1.0.1.1-a8_oqTyH0jw_XiAjsSpqyuvmevUDtFlFF3qP1bTLkYM",cFPWv: 'b',cITimeS: '1739782325',cTTimeMs: '1000',cMTimeMs: '120000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/search?q=finite%20element%20method&__cf_chl_f_tk=8snPJkpV02WwymthlRs6sg1Th5dCHWe394dSJUYKqg0-1739782325-1.0.1.1-a8_oqTyH0jw_XiAjsSpqyuvmevUDtFlFF3qP1bTLkYM",md: "6RkIHRhE4rmUHaa1ECQpLPkufEbYUd8tFoXf651aZJg-1739782325-1.2.1.1-JZ9LzSTT4LOqHTJVCQTt5XLtggcbKFI52oskQYeCKtaDcnjtFW4UxEk7bIsOcI.pcIWGsvSL6WX0_t11QQltuXJxOfdCiXUxUBXOEDhptvvf1taIQBTBYNgJJ7tj8gfgx2iDF8JgDG2.Di3oYvlnmQyp9ZOpGpIOcNXzSBdjorJnuQFQ65IYT2Tv853VIP9ffN7.QkuW9Z5lQJ7STZt4ZXnZv.cmn2keLHLkT2UHUlp_Q1jITaDtp8lVLVrkTNeuX8LpEH0Jckc2XC6n2do_uBpBa_vDH9JBInjmdj0gxTknFp3TW9yiLAKp02FMOSRKDMvRk0C6EgfOHbtCxg7Vmq2MbUV7kfSexswzUZyN_jzRM48fhSYK7tAmxIhKCUQG.emLxRKCWzApvlWRQrcSVK86lDeYRBvy3zz4w0zXmVN09eHR2jCXBx5DKipcGbF2Y6u7obmXFRNQYY5x1awaWP_ZOmlEOn8kJZynqD700NUfL9YesF9QZHogKkNEODKYtHqr2fqA3OYIH_sthIauYh_Qz98IXIs7MCfzFkSZBV9X6TfZ0OfshmGu6SExO8uofXxG1w_g_jo4i7IH3DmN7wjp8f0nKewuQ1x5rjUIoW1fwkRy5LyTu8S6QAxv_YgdxaezRURFQ4cUM3YyJPXlVcc4eQl1GD3vri6Awjc5WZetyisBkE7kmWdywS5wsQJ6eTOzHTeiCeCjuQRKoTwb7c6ORyCfC4cvMj_X68TYR78rvtxhRtxVjA5uCVv4RP9qLgMENJ.CMyHK7dxTcnayBbAGFNpguRxi9xHUur5YiYBETataGiu1MZfhXLRmgdpIfD3gIBmv8dxFQ30UeqrDZWF85.KR3pjbIatg.TAP1Cv3Qnz1ZUfyqFjEqr.X7xgbdAwK1QP7aGU5XpU5aLp4stWOCdWlvSMgu8g.LNMGaIdhz9q2vKc3S.RelJcUlVMgLBsbg5e7AXYsfSRWG0IpYIuu8oF0nC8j1l3BaNzd5EW2r1Dw7BZMuXQIfqWuHPTnw3L7RqbncTOngsozvX94mexJ7JxbsfcM73smzNzWB7cMetA9Eh3A97mAFx8I0dTx3opVizjS8iEzp_md8VLML6vRsIy212BGtlaDOtEK7M5dpCJCNaGAFLp1q4WhUAF08q9TOvMgtGFwfiYNJMTfxmFpiBjtXab4cXkGJ7uNhRMq6sw9NShr2Y.eRVIfUq5durcvhYKjxk5sOpKBGX0wzUKu8vP7WtS2Ysq9m5UMCIsyPUmvZpb2gibtDZfW8EKuztMHrNDjrO9d_2Bfyd23TrxLq.SW.v7k6.fwoFnDGttzsEZ5Lsb7WNHmSS8L5AyVZwIJ7gZme8Roafp9qvxTTjepwZf7qgpEFPafm1XQ6dWnuQfzCb9wzXxm1JIetGuopfUpyKpiW2T7.rVGAqL20DigkFwl8zOflPvlkPKnybySEJanFndsNmDVBJBpC4sGj.Ieu2vb5OBNr13dWVQgOifFXtSIa9NwRLMdhdwGynnCfHEvXxvognNYfzI7m8OSA9H0b5PfXaTIH0Cdzz2wkwdsoLF8oFjq14xIbnc55_yb5JjGQXPSW6xAd2SIJp7IDAzZQ3tFPicnzvjRcjQac8p0Qgty4yk0b.iC0wbFZYOFVp8qKZYHP_v5lWxu4Dz1uj2Q2Ny_4XxHnpqTwzV3q8uZ7dWjHAJMCnnSE1e50iB8WgIqyiSBpnmfHq0XxhZv3DT8Xz4wn3frmoYujkY3Voygm0nyo0QmvctrtMSoMYXi2yD2e3I16Lwc0hkPw_OfKqH8W1bPSJgZ8VBplMdeRWqDEbuhGOE6O.6E.72YD043H9llluO5TXpb1nJ.m8E_t64OC.v.I1HdjuCfuwXQvitK4xrrBlCJZCYowTQ_dErZNfEvLQG7EV6AqoalpGKXTOLU5GWLkFwsqN6HrXslDB.6nxOQ5EZeenVAcVgIGZo",mdrd: "M7FzG7gyhdIQq9150w7zkdbLa5EuwpJc0hZ10MdzY34-1739782325-1.2.1.1-EseYY7WtQodfqvYjLGhFfAyI8xv813s2uCavfMUAbIo_YUbYTXnzvKCukq.Foca7JitEreFPtDDJGcB.mgDWXf3RUGKuARwHHfk_9ZpBeIXaVxim5fcFAyQRljPCmXkSPHILDy8FzouSxeofdI_iGbPNWBOHbVitumVD6e_lAGDIIuVtvBsQN8jbZaebjHnho4aXDDx7aN_dtGlIlu3qVYfY_OepanG3P90t1Jn7oR4XvRBY2WvbURSv0ivVAmQccZ9mnTwbLP6dPkNS8Xu1HMotADMpj6ssMYi0N_SK_iub9mzXh6Bc_gTxRYPjxPDt96xT8m_ncsuKtzPv81pjHxxBmDyMHAs24VXU1hxS_C9GjmRMoawSRJnorePTHFIj6720eCfnLAb2Ml8D5L0K0crMh82ot_g9APZf5BSAdA7AVrFsHN2AWzGkbbM4OtPtieYTpINoRP2C4uLUP5e7fhYubYqy.Yae7UVgC1U0b6IrVweeGDI3yBBKQRWHIwhbjJWWncUsmSVT.gCq77HcNPRAnYGhAuPQhs.W71uQoQ8B13GpwBo0kCmUXbqoYwn06U7GOz9NL8RcowL_l4p2EUjT7OU7Xe00E_9g1ua2rywGB7TDXenX.0Q8ybGesg1V.wZTUevxvXQf27oy..v537_3wqmPpGa4M0hKb8ORrg2U9R45qaDNxiQJin1rNh8AvLMGYm_4ZAwwM9swx.9xXNgKkI.ErUpqK56a6ITDRdEqZriVesmVy3rXvxhL_HlyJFd5zuZJxKwqkfIS_tRRmbakB6tgB7AQZOdCJE1gqeAJGiZWze0eXwjD8JOQiVPf1ymyMl3Sr3f31XVTIOrbU.1wwHtNvIaH2rdLYiiG7nw4N.yBn.dMTQ_Lnf31CK3bZG9M1I6l4lT4OVCXjxXGLrIlIuc_MnjmrlGnGRayOGu89idld.v5_8UdNZzmydF1fdTbTJDD9ln6TWaTgAM8wgRNDwgNgQOKalu5Z09G7mRoQVqKCgeGWXF8WtcND2c1zHW4L0O43ezrPgiPDtWJK7pQ_Jv.S6VCqdLzvaK2_NTXjHGaJNZvhFb2cE.CKpd4uTnOkE5NWmiU9eE0mwCI0yYYMTkH1gjMbDv_a_gxz4Z1.K1Iwnu8EAay_VUuldT9eX_bW3SZ0J_LgsnrL83FJZ2tXqnQ.de9JkZELmTV18gIK9lZemD0g.4tkM_fRcnrPJgSZcSdKudntqrRWmSI8XP_8O8UTKonMY7eDtREutV2M.NvF.eSsodVxL1W.li6x_CGAZcyAzcrpWynpSjU1PgJ28.WCBSHMkmlfsnm_cJPiBLA7rtBtp0pEDMCbfMTRP.pdxGWSSQzBEai3xgCE63im_1XMNZ19LAKwULporARjY6x6556Ing1R3VFTm5Um08pp9lO0wpCc1HN2eXww5Smi9ABVne81ZCxfI0N2wA3EKZWjNbqrsnoLd38pTaTYH1ajde1CjGLC1y0QnNSsmjyYWUehpi349hUGGpP3XBs9ygOuA2VXQCIOWv64E4lWjRBWmzMkHRSqDO07ClLWTp4KVCgbjHOBM3PPIDWumZanci0pCGBectPVRQaIUMW.8miHJE_HBcONtFfB9UL4yn1dijG59ouIlFgxVECF1KZpfKi0WDZYWUto1xcxFDydj__A0ryivjaXUzjXP34pSzcleiKbqQgJQXzdfGPoojFo71qitTT9XPIkPBwCJSnaxwamZFrmZ4L0Z_usVSwp5lk16HKRfcsJWYhOigwY21vZFR5NkNpy_w1t3u5afCcJ_wXON9hgzI4jPDHKbqiwnjTdJQx9MNrQZHfAklS4vYlkPE1I02fHQ7XnmxFobAlAA6AzKx7jGRKyvToe6qvPS4HGfp2T52b2Z328NcPPNw0cgz7zoaNM6ITZ4gHMrriMTP8bs8Po6TRR3b7qQWenz8BJclMKkpLnJq2IN9jhm0S7bBraUXBx6PHO8RGtY00bU2FjrRSv_FzPICIw7MDAQ"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=91348a0e3c0ffce3';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/search?q=finite%20element%20method&__cf_chl_rt_tk=8snPJkpV02WwymthlRs6sg1Th5dCHWe394dSJUYKqg0-1739782325-1.0.1.1-a8_oqTyH0jw_XiAjsSpqyuvmevUDtFlFF3qP1bTLkYM" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>