onsider the variational form a(u,v) = (f,v) where a(u,v) = 'u'v' dx Prove that VvE H(0, 1), i = 1, 2,...., n - 1 a(v,q)=-v(x-1) + 2v(x) = v(x+1)] h - where (,), CV, is usual basis of hat functions Q2: A: Consider the problem A²u = f and u= ди On = 0 on an With bilinear form a(u,v) = f Au. Av dn prove that a(u,v) V-ellpitic. B: Prove that Where lu-ulls Chulz lul = a(u, u) = f vu.vu dx + fonu. uds Q3: Consider the problem -V. (Vu) + u = 0, in n.Vu=gN on an 1- Show that the solution u of the problem satisfies the stability lulul≤ Clignlin (use 2ab
onsider the variational form a(u,v) = (f,v) where a(u,v) = 'u'v' dx Prove that VvE H(0, 1), i = 1, 2,...., n - 1 a(v,q)=-v(x-1) + 2v(x) = v(x+1)] h - where (,), CV, is usual basis of hat functions Q2: A: Consider the problem A²u = f and u= ди On = 0 on an With bilinear form a(u,v) = f Au. Av dn prove that a(u,v) V-ellpitic. B: Prove that Where lu-ulls Chulz lul = a(u, u) = f vu.vu dx + fonu. uds Q3: Consider the problem -V. (Vu) + u = 0, in n.Vu=gN on an 1- Show that the solution u of the problem satisfies the stability lulul≤ Clignlin (use 2ab
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![onsider the variational form a(u,v) = (f,v) where
a(u,v) = 'u'v' dx
Prove that VvE H(0, 1), i = 1, 2,...., n - 1
a(v,q)=-v(x-1) + 2v(x) = v(x+1)]
h
-
where (,), CV, is usual basis of hat functions
Q2: A: Consider the problem A²u = f and u=
ди
On
= 0 on an
With bilinear form a(u,v) = f Au. Av dn prove that a(u,v) V-ellpitic.
B: Prove that
Where
lu-ulls Chulz
lul = a(u, u) = f vu.vu dx + fonu. uds
Q3: Consider the problem
-V. (Vu) + u = 0, in
n.Vu=gN
on an
1- Show that the solution u of the problem satisfies the stability
lulul≤ Clignlin
(use 2ab <a² + b²).
the lingon form ((12) continuous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9b32f1a-d31b-4d65-8e68-013365b98e60%2F9c11d545-d103-43b1-a768-f77ed293cdbc%2F5anrod_processed.jpeg&w=3840&q=75)
Transcribed Image Text:onsider the variational form a(u,v) = (f,v) where
a(u,v) = 'u'v' dx
Prove that VvE H(0, 1), i = 1, 2,...., n - 1
a(v,q)=-v(x-1) + 2v(x) = v(x+1)]
h
-
where (,), CV, is usual basis of hat functions
Q2: A: Consider the problem A²u = f and u=
ди
On
= 0 on an
With bilinear form a(u,v) = f Au. Av dn prove that a(u,v) V-ellpitic.
B: Prove that
Where
lu-ulls Chulz
lul = a(u, u) = f vu.vu dx + fonu. uds
Q3: Consider the problem
-V. (Vu) + u = 0, in
n.Vu=gN
on an
1- Show that the solution u of the problem satisfies the stability
lulul≤ Clignlin
(use 2ab <a² + b²).
the lingon form ((12) continuous.
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