title: A POSTERIORI ANALYSIS OF ITERATIVE ALGORITHMS FOR A NONLINEAR PROBLEM. 2013. &#x27E8;hal-00918226v2&#x27E9;
text: ❝r✐t❡r✐♦♥✱ ✷✵ ❇❊❘◆❆❘❉■✱ ❉❆❑❘❖❯❇✱ ▼❆◆❙❖❯❘ ❆◆❉ ❙❆❨❆❍ Uniform Error Adapt Error Log(Error) Number of iterations New Class Refinement level Number of vertices ❊rr♦r ❝✉r✈❡ ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ✈❡rt✐❝❡s ♥✉♠❜❡r ❢♦r λ = 10 ❛♥❞ p = 1✳ ❯♥✐❢♦r♠ ❡rr♦r ✭t♦♣✮✱ ❛❞❛♣t✐✈❡ ❡rr♦r ✭❜♦t✲ t♦♠✮✳ ◆✉♠❜❡r ♦❢ ✐t❡r❛✲ t✐♦♥s ❛s ❛ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ r❡✲ ✜♥❡♠❡♥t ❧❡✈❡❧ ❢♦r λ = 10 ❛♥❞ p = 1✳ ❈❧❛ss✐❝❛❧ ❝r✐t❡r✐♦♥ ✭t♦♣✮✱ ♥❡✇ ❝r✐t❡r✐♦♥ ✭❜♦tt♦♠✮✳ ❋✐❣✉r❡ ✶✻✳ ❋✐❣✉r❡ ✶✼✳ ✻✳✸✳ ❈♦♠♣❛r✐s♦♥ ♦❢ t❤❡ ❛❧❣♦r✐t❤♠s✳ ■♥ t❤✐s s❡❝t✐♦♥ ♦✉r ♣✉r♣♦s❡ ✐s t♦ ❝♦♠♣❛r❡ t❤❡ ✜①❡❞✲♣♦✐♥t ❛❧❣♦✲ r✐t❤♠ ✇✐t❤ t❤❡ ◆❡✇t♦♥ ❛❧❣♦r✐t❤♠ ✉s✐♥❣ ❛❞❛♣t✐✈❡❧② r❡✜♥❡❞ ♠❡s❤❡s✳ ❋✐❣✉r❡ 18 ✐❧❧✉str❛t❡ t❤❡ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ◆❡✇t♦♥ ❛❧❣♦r✐t❤♠ ✇✐t❤ ❛♥ ✐♥✐t✐❛❧ ❣✉❡ss u0h = 0.03✳ ❲❤❡♥ ❝♦♠♣❛r✐♥❣ t❤❡ t✇♦ ♠❡t❤♦❞s✱ ◆❡✇t♦♥✬s ♠❡t❤♦❞ r❡q✉✐r❡s ♦♥❧② t✇♦ ✐t❡r❛t✐♦♥s ❢♦r ❛❧❧ ❝♦♥s✐❞❡r❡❞ r❡✜♥❡♠❡♥t ❧❡✈❡❧✱ ✇❤❡r❡❛s t❤❡ ✜①❡❞✲♣♦✐♥t ❛❧❣♦r✐t❤♠ r❡q✉✐r❡s 10 ✐t❡r❛t✐♦♥s ✐♥ t❤❡ ✜rst r❡✜♥❡♠❡♥t ❧❡✈❡❧ ❛♥❞ ❞♦❡s ♥♦t ❣♦ ❜❡♥❡❛t❤ 4 ❢♦r t❤❡ r❡st ❧❡✈❡❧s✳ ■t ✐s ❝❧❡❛r t❤❛t t❤❡ ♠❡t❤♦❞ ♦❢ ◆❡✇t♦♥ ❛✈♦✐❞s ♣❡r❢♦r♠✐♥❣ ❛♥ ❡①❝❡ss✐✈❡ ♥✉♠❜❡r ♦❢ ✐t❡r❛t✐♦♥s✳ Number of iterations FPA NA Refinement level ◆✉♠❜❡r ♦❢ ✐t❡r❛t✐♦♥s ❢♦r t❤❡ ♥❡✇ st♦♣♣✐♥❣ ❝r✐t❡r✐♦♥ ♦♥ ❛❞❛♣t✐✈❡❧② r❡✜♥❡❞ ♠❡s❤❡s ✇✐t❤ γ = 0.001.