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gradient of divergence
Posted 2014年4月20日 GMT-4 08:55 Parameters, Variables, & Functions Version 4.4 2 Replies
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Hi all,
Is it possible to represent the gradient of the divergence of a vector field in the Coefficient Form PDE other than using the Weak Form?
Thanks,
Tony
Is it possible to represent the gradient of the divergence of a vector field in the Coefficient Form PDE other than using the Weak Form?
Thanks,
Tony
2 Replies Last Post 2014年4月21日 GMT-4 06:21
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Posted:
1 decade ago
Definitely you can. But I think you need to somehow manipulate the form of the expression in order to do that.
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Posted:
1 decade ago
Thanks Pu.
We have:
grad div F = [F1xx+F2yx, F1xy+F2yy]; (1)
div(c*grad F) = [c11*(F1xx+F1yy)+c12*(F2xx+F2yy), c21*(F1xx+F1yy)+c22*(F2xx+F2yy)] (2)
where c=[c11, c12; c21, c22], hence, it seems to me that mixed partial derivative terms in (1) never appear no matter how to choose the coefficient c if we use the Coefficient Form PDE to represent the gradient of divergence. Am I correct?
Thanks,
Tony
We have:
grad div F = [F1xx+F2yx, F1xy+F2yy]; (1)
div(c*grad F) = [c11*(F1xx+F1yy)+c12*(F2xx+F2yy), c21*(F1xx+F1yy)+c22*(F2xx+F2yy)] (2)
where c=[c11, c12; c21, c22], hence, it seems to me that mixed partial derivative terms in (1) never appear no matter how to choose the coefficient c if we use the Coefficient Form PDE to represent the gradient of divergence. Am I correct?
Thanks,
Tony