Nonzero entries of dentical to finite difference Actually, not quite identical; the FEM matrit is h times the finite difference matric. Obviously, one of the the advantages of the FEm to develop ap- triangulations Th of arbitrary dome eercised in this example. Our purpose rather is to get some sense of how the y;“ interact” to form A 3 Theoretical Analysis 3.1 General results Nor SLIDE 17 Recall llI=a(u, D)=(2(9)=/ Vu12dA Then ah is the projection of u on Xh The proof is identical to that for the one-dimensional case 1.2 H Norm SLIDE 18 H1(g2) Vul+02dA Then l Ju -wnI B: continuity constant(=1)×✥Ø❋Ù✎Ú✪ÛÝÜ✔Ø■Û✪Ù❢Þ✗Ü✔ß✱ÛÝà❂Ø❈á Ü✗Ø✯â➔ã❇Ø❈á▼äå✾æ ß❀ç✜ÛÝÙ❋Þ✗ß✱èÝé✛ê✌Þ✗Ø✐ë❱Ù✎ß✳Þ✗Û➊ç✜ß✻ì❏ÛÝÜ✔ÛÝÙ✾è✄Û✖à✪í î✑ï✄ð✞ñ✾ò✯ó★ó➓ô✴õ✑ö❏÷✯ð✠ø✄ñ✜ù★ð❃ú❄ù✷û❈ú✪ö✾ð✞ù✷ï✗ò✛óýü✆ð★þ✾ú✐ÿ✁￾✄✂✆☎✹ò✯ð✞✝✣ù✠✟ ù☛✡✌☞✎✍❞ð✞ù✏☎❆ú✑✡✹ð★þ✾ú✓✒➣ö❱ù★ð❝ú û✯ù✔✭ú✕✝✔ú✪ö❏ï✙ú ☎✹ò✯ð✞✝✣ù✠✟✗✖✙✘✓✚✕✛Ýù✷÷✛ñ✜✡✣ó➓ô✴õ✹÷✛ö❏ú ÷✣✢✁ð★þ✾ú❞ð✩þ✎ú ò❈û✤✛✯ò✯ö❱ð❝ò✦✥❋ú✑✡❍÷✣✢✁ð✩þ✎ú ÿ✁￾✄✂★✧ ð❝÷➟û❈ú✕✛✴ú✪ó✻÷✪✩➙ò✪✩✬✫ ✩✭✝✗÷✕✟❋ù✏☎❆ò✛ð◗ù✷÷✛ö✮✡✯✚✙ò✰✡✪ú✙û✁÷✯ö✱✥❢ú✪ö❏ú✕✝✔ò✯ó●ð✲✝✣ù✷ò✛ö✗✥❈ñ✜ó✻ò✯ð✞ù✷÷✯ö✳✡✵✴å ÷✶✢➊ò✤✝✕✚✪ù★ð✲✝✗ò✤✝✣ô✁û❋÷✤☎✹ò✯ù★ö✳✡✯✧ ù☛✡❧ö❏÷✯ð ú✪✟❢ú✕✝✔ï✪ù☛✡✪ú✗û✁ù★ö ð✩þ✶ù☛✡✹ú✷✟✶ò✸☎✓✩✌ó✻ú✦✖✹✘❂ñ✺✝✻✩✌ñ✺✝✞✩✎÷✤✡✄ú✼✝✔ò✯ð✩þ✎ú✕✝■ù☛✡✐ð❃÷✽✥❋ú✪ð✾✡✪÷✤☎✹ú✿✡✪ú✄ö✳✡✄ú❄÷✣✢✆þ✎÷✤❀ ð✩þ✎ú ❁✁❂✹❃ù★ö✾ð❃ú✕✝✔ò❈ï✪ð❅❄✆ð❝÷✓✢✄÷✤✝❅☎ äå ✖ ❆ ❇❉❈❋❊✓●✯❍■❊✾❏✁❑✕▲✻▼❖◆◗P❙❘❋▼❖◆❅❚❱❯✁❑✑❯ ❲✾❳✶❨ ❩❭❬❫❪✓❬❵❴✳❛✁❜❞❝❡❬❫❢✜❣❤❜❥✐✮❢ ❦❫❧♥♠✭❧♥♠ ♦q♣sr✉t✤✈✎✇◗①③②✎t✤④ ⑤✭⑥✗⑦✏⑧❫⑨◗⑩✗❶ ❷➍Û✖è✪é✛ê✱ê❹❸❺❸❻❸ ❼✬❸❺❸❺❸ ✍❤❽❿❾✬➀❼✭➁✶❼✺➂❹➃➄❸ ❼➅❸ ✍➆✻➇✑➈❻➉✳➊ ➃➌➋➉ ❸ ➍✯❼➅❸ ✍➏➎ä❉➐ ➑✾➒✎ÛÝÙ ❸❺❸❺❸ ➓✺❸❺❸❻❸➔➃ ß✱Ù✜á →✬➣✸↔➔↕■➣ ❸❻❸❺❸ ➙❱➛➝➜å ❸❻❸❺❸ ➀ ➓➞➃❭➙❱➛➝➙ å ➂q➟ ➙ å ß✱à❂Þ✪➒✎Û ✩✭✝✗÷❥➠✪ú✙ï✄ð✞ù✷÷✯ö Ø✛á➏➙❞Ø❋Ù❋➡å ß✱Ù Þ✷➒✎Û✆ÛÝÙ✎Û✪Ü✪➢➔➤❛Ù✾Ø❈Ü✪➥✁í ➦þ✎ú✓✩✭✝✗÷Ý÷✶✢✆ù☛✡ ß✱ç✜ÛÝÙ❢Þ✔ß❀è✪é✛ê ð❝÷❛ð★þ✾ò✯ð✬✢✄÷✤✝✆ð✩þ✎ú■÷✯ö✌ú✑✫❑û✛ù✏☎❆ú✪ö✮✡✣ù✷÷✯ö✌ò✯ó✟ï✙ò✰✡✪ú✦✖ ❦❫❧♥♠✭❧☛➧ ➨➫➩✌①③②✎t✤④ ⑤✭⑥✗⑦✏⑧❫⑨◗⑩➔➭ ❷➍Û✖è✪é✛ê✱ê❹➯❅❼➅➯ ✍➆➇ ➈❻➉✳➊ ➃ ➋ ➉ ❸ ➍✯❼➅❸ ✍✾➲ ❼ ✍■➎ä➳➐ ➑✾➒✎ÛÝÙ ➯✑➓✺➯ ➆➇ ➈❻➉✎➊➸➵➻➺❵➼ ➲➾➽➚❤➪ ß✻Ù✎á →➣ ↔➔↕➣ ➯✑➙✽➛➝➜å ➯ ➆➇ ➈❺➉✳➊ ➟ ➚ æ è✄Ø✶Û✪Ü✙è✄ß❺➶✶ß✳Þ✣➤❛è✪Ø❈Ù✾à❑Þ✗é❈Ù❢Þ ➀✶➹➴➘ ➂❅➟ ➽ æ è✄Ø❋Ù❋Þ✗ß✻Ù✜➷✎ß✻Þ✣➤❄è✪Ø❈Ù✾à❑Þ✗é❈Ù❋Þ ➀ ➃ ➼ ➂✣í ➦þ✎ú✻✩✭✝✔÷✖÷✣✢❧ù☛✡ ß✱ç✜ÛÝÙ❢Þ✔ß❀è✪é✛ê ð❝÷❛ð★þ✾ò✯ð✭✢✄÷✤✝❧ð✩þ✎ú■÷✯ö✌ú✑✫❑û✛ù✏☎❆ú✪ö✮✡✣ù✷÷✯ö✌ò✯ó♦ï✗ò✤✡✪ú✦✖ ➬