1 Model problems 1.1 Dirichlet 1.1.1 Strong Form SLIDE ain:9=(0,1) Find a h that in Q (1) 1.1.2 Minimization statement Define X≡H(9) Find he w2 d-f This follows from the previous lecture, noting that dA is now dz, and vw 1.1.3 Weak Formulation sLIdE 3 Find u∈ X such that 6J(u)=0 u∈X f vdx Vu∈X Again, this follows f er lecture with Vu. Vu now given by ur Ux❇ ❈❉❋❊❍●❏■▲❑◆▼☞❉P❖❍■✒●❏◗❙❘ ❚☞❯❱❚ ❲❨❳❱❩❬❳❱❭❫❪❏❴❛❵✡❜ ❝❄❞❡❝❄❞❡❝ ❢✡❣✐❤❦❥❄❧✝♠♦♥✝❥❬❤❦♣ q❄rts✈✉✣✇②① ③⑤④⑦⑥⑨⑧❶⑩❸❷✡❹ ❺✢❻❽❼❡❾➀❿➂➁✸➃➅➄ ➆✌⑩➇❷❫➈➊➉➌➋❱➍❬➎➐➏✻➑➒➏❫⑧❦➑ ➓ ➉❅➔✸➔→❻ ➣ ⑩❸❷↔❺ ➉✽❼❡❾↕➃➙❻ ➉✌❼❱➁✸➃➙❻ ❾ ❿ ➛④⑦➜➞➝↕⑩➇➟↕➠✐❷➡➣✌➄ ❝❄❞❡❝❄❞➤➢ ➥◆➦❡❧✌➦❡♣✘➦❀➧⑦➨➩❣✸➦❡❥❄❧✢❢✡❣➂➨➩❣✸➫t♣▲➫t❧❅❣ q❄rts✈✉✣✇➯➭ ③⑤➠✒➲❬❷➀➠ ➳➸➵➻➺➽➼➾ ❼❀❺➞➃➅➄ ➆✌⑩➇❷❫➈ ➉✻❻✤⑧❶➜➚➝✘⑥➪⑩➇❷ ➶✌➹⑦➘➷➴ ❼❡➬⑤➃ ➮➏➀➠➂➜➒➠ ➴ ❼➱➬⑤➃✟❻ ➁✃➻❐ ➼ ➾ ➬❏❒➔❏❮⑦❰ ➓ ❐ ➼ ➾ ➣❄➬ ❮⑦❰♦Ï Ð❅ÑÓÒ➤Ô✗Õ✒Ö❦×✈×➇Ö❶Ø✽Ô➅Õ➐Ù➒Ö❶Ú✜Û✈Ñ❬Ü✔Ý❅Ù➒Ü✐Þ➂Ò❡Ö❶ßÓÔ✻×➇Ü➐à✐Û❀ß➩Ù➒Ü✒á✗â❄Ö❦ÛãÒ✈âtä➽Û➱Ñ➀å❶Û ❮tæ Ò➤Ô✴â❄Ö❶Ø ❮↕❰ áçå❦â❅è✚éç➬êÒ➤Ô â❄Ö❶Ø♦➬➞➔❫ë ❝❄❞❡❝❄❞❸ì íî➫t➨➀ï②♥✣❥❫❤❦♣➽ð✌ñ❡➨➀❣➂➦❡❥❄❧ q❄rts✈✉✣✇➯ò ➆✌⑩➇❷❫➈➊➉❍ó✚➳ ➋❱➍❫➎➐➏✻➑➚➏❬⑧❦➑ ô ➴↕õ ❼➱➉ö➃÷❻✤❾✻❿ øçù❋ó✧➳ ú ❐ ➼ ➾ ➉❄➔ûù❶➔ ❮↕❰ ❻ ❐ ➼ ➾ ➣✵ù ❮⑦❰ ❿ ø✵ù✴ó✧➳ Ï üä↕å❶Ò✈â➀á÷Û➱ÑÓÒ➤Ô✱Õ✒Ö❦×✈×❸Ö❦Ø✽Ô✱Õ➐Ù➒Ö❶ÚýÖ❶ß➩Ù✵Ü➚å❶Ù☎×þÒ❡Ü✐Ù✵×➇Ü➐à✒Ûãß➩Ù➒Ü✵Ø☞Ò✈Û✈Ñ✻éÿ➉✁￾➂éÿù â❄Ö❦Ø✘ä⑦Ò✈Þ Ü✐â✄✂✆☎✔➉➔ ù➔ ë ➁