Estimation of relation between vertices of a triangle
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Let $hat{t}$ be the reference triangle with the vertices $hat{A_1} = (0,0)$, $hat{A_2} = (1,0)$, $hat{A_3} = (0,1)$ and let $t$ be the triangle with the vertices $A_1 = (0,0)$, $A_2 = (h_1, 0)$ and $A_3 = (0, h_2)$. Let $hat{u} := u circ F_t$, where $F_t: hat{t} to t$ denotes the affine map with $F_t(hat{A_i}) = A_i$ for i = 1, 2, 3.
In my script, I read that the following estimate holds true:
$$ |u|_{H^k (t)} leq C^k h_t^{1-k} |hat{u}|_{H^k (hat{t})}$$
where $h_t$ is the diameter of the triangle $t$.
Why does this estimate hold true?
geometry numerical-methods estimation triangulation
asked Nov 19 at 7:48
StMan
1387
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0
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Let $hat{t}$ be the reference triangle with the vertices $hat{A_1} = (0,0)$, $hat{A_2} = (1,0)$, $hat{A_3} = (0,1)$ and let $t$ be the triangle with the vertices $A_1 = (0,0)$, $A_2 = (h_1, 0)$ and $A_3 = (0, h_2)$. Let $hat{u} := u circ F_t$, where $F_t: hat{t} to t$ denotes the affine map with $F_t(hat{A_i}) = A_i$ for i = 1, 2, 3.
In my script, I read that the following estimate holds true:
$$ |u|_{H^k (t)} leq C^k h_t^{1-k} |hat{u}|_{H^k (hat{t})}$$
where $h_t$ is the diameter of the triangle $t$.
Why does this estimate hold true?
geometry numerical-methods estimation triangulation
asked Nov 19 at 7:48
StMan
1387
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $hat{t}$ be the reference triangle with the vertices $hat{A_1} = (0,0)$, $hat{A_2} = (1,0)$, $hat{A_3} = (0,1)$ and let $t$ be the triangle with the vertices $A_1 = (0,0)$, $A_2 = (h_1, 0)$ and $A_3 = (0, h_2)$. Let $hat{u} := u circ F_t$, where $F_t: hat{t} to t$ denotes the affine map with $F_t(hat{A_i}) = A_i$ for i = 1, 2, 3.
In my script, I read that the following estimate holds true:
$$ |u|_{H^k (t)} leq C^k h_t^{1-k} |hat{u}|_{H^k (hat{t})}$$
where $h_t$ is the diameter of the triangle $t$.
Why does this estimate hold true?
geometry numerical-methods estimation triangulation
asked Nov 19 at 7:48
StMan
1387
Let $hat{t}$ be the reference triangle with the vertices $hat{A_1} = (0,0)$, $hat{A_2} = (1,0)$, $hat{A_3} = (0,1)$ and let $t$ be the triangle with the vertices $A_1 = (0,0)$, $A_2 = (h_1, 0)$ and $A_3 = (0, h_2)$. Let $hat{u} := u circ F_t$, where $F_t: hat{t} to t$ denotes the affine map with $F_t(hat{A_i}) = A_i$ for i = 1, 2, 3.
In my script, I read that the following estimate holds true:
$$ |u|_{H^k (t)} leq C^k h_t^{1-k} |hat{u}|_{H^k (hat{t})}$$
where $h_t$ is the diameter of the triangle $t$.
Why does this estimate hold true?
geometry numerical-methods estimation triangulation
geometry numerical-methods estimation triangulation
asked Nov 19 at 7:48
StMan
1387
asked Nov 19 at 7:48
StMan
1387
asked Nov 19 at 7:48
StMan
1387
asked Nov 19 at 7:48
StMan
1387
asked Nov 19 at 7:48
StMan
1387
1387
add a comment |
add a comment |
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