- #1

zoltrix

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aside from some constraints such as an irregular integration domain, can FDM solve any type of PDE same as FEM ?

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- Thread starter zoltrix
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- #1

zoltrix

- 34

- 3

aside from some constraints such as an irregular integration domain, can FDM solve any type of PDE same as FEM ?

- #2

jedishrfu

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I’m guessing PDE is for partial differential equations.

- #3

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- #4

bigfooted

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Note that there are many finite element methods and many finite difference schemes. A specific Finite Element Method is limited in the types of equations that can be solved by it, just as a specific Finite Difference Method is limited in the types of equations that can be solved with it.

- #5

zoltrix

- 34

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same as the Runge Kutta method, for example, which is applicable to all types of ODE

is it just a matter of accuracy or some PDE schemes may be unstable for some type of PDE ?

as far as I know all FEM schemes yield results even though some are more accurate or faster than others depending upon the shape of the integration domain

- #6

Frabjous

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You are holding FDM to a much higher standard than FEM.so, do you mean that it does not exist an universal FDM scheme which fits all types of PDE ?

as far as I know all FEM schemes yield results even though some are more accurate or faster than others depending upon the shape of the integration domain

Asking in full generality is probably hindering the response to this question because people are worried about edge cases. Be more specific about what you are concerned about.

- #7

zoltrix

- 34

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a common classification is : elliptic-parabolic-hyperbolic

is FDM suitable for all these types of PDE ?

- #8

Frabjous

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Yes

- #9

zoltrix

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solver(eqn,a,b,c,d...)

or at least a specific "solver" for each type of PDE's whereas "eqn" is the generic partial linear differential equation of second order and a,b,c,d... its parameters ?

if so , can you suggest a book or a website ?

- #10

bigfooted

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http://hplgit.github.io/

https://hplgit.github.io/fdm-book/doc/web/index.html

https://hplgit.github.io/fdm-book/doc/pub/book/html/decay-book.html

http://hplgit.github.io/num-methods-for-PDEs/doc/pub/index.html

http://hplgit.github.io/num-methods-for-PDEs/doc/pub/nonlin/html/nonlin.html

- #11

zoltrix

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Thanks bigfooted

it is exactly what I was looking for

it is exactly what I was looking for

- #12

Chestermiller

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- #13

bigfooted

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http://hplgit.github.io/INF5620/doc/pub/H14/fem/html/main_fem.html

https://fenicsproject.org/

- #14

zoltrix

- 34

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what is the advantage ,if any, of FDM / FEA over Mathematica / Maple to solve partial differential equations ?

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