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Results tagged with numerical-analysis-of-pde
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user 61771
2
votes
Accepted
Weird claims and conclusions in "Introduction to Shape Optimization"
Not an answer, but too long for a comment. The general idea with this stuff seems to be to pair your family $\mathscr{D}$ of admissible domains with a(ny) suitable normed-space $\mathscr{V}$ of vector …
- 778
1
vote
Accepted
Prove of the shape-derivative identity relating the shape and material derivative of a shape...
The classical material derivative $D\varphi/Dt$ of a test function $\varphi \in C_c^\infty(\mathbb{R}_+\times D)$ is obtained by setting
$$
\dfrac{D\varphi}{Dt}(x) := \dfrac{\partial\tilde\varphi}{\pa …
- 778