Solving Variational Equations with FreeFem++

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In summary, the conversation discusses the use of freefem++ to solve problems with finite elements method and the use of a specific form of the variational equation. The person is looking for a book or source to study this form of the equation.
  • #1
urric
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Hi, sorry if this isn't the correct forum.
I'm trying freefem++ to solve some some problems with finite elements method, but in the documentation the following form of the variational equation is used:

[itex]\displaystyle\int_{T_{h}} (\frac{{\partial u}}{{\partial x}}\frac{{\partial v}}{{\partial x}} + \frac{{\partial u}}{{\partial y}}\frac{{\partial v}}{{\partial y}} )dxdy =\displaystyle\int_{T_{h}} fvdxdy[/itex]

I've searched for that form, but I wasn't able to find it

Could you tell me about a book or any source where I can study that form of the variational equation?

Thanks
 
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  • #2
Looks strange without any imaginary units, time parameters or simply the order in the integral on the LHS.
Some context would be more than helpful.
 

FAQ: Solving Variational Equations with FreeFem++

What is FreeFem++?

FreeFem++ is a finite element software designed for solving partial differential equations (PDEs) and variational problems. It is widely used in the scientific community for its efficient and accurate numerical solutions.

How does FreeFem++ solve variational equations?

FreeFem++ uses the finite element method to discretize the variational equations into a system of linear or nonlinear equations. It then applies iterative methods, such as Newton's method, to solve the system and obtain the numerical solution.

What types of variational equations can be solved with FreeFem++?

FreeFem++ can solve a wide range of variational equations, including elliptic, parabolic, and hyperbolic PDEs, as well as variational problems in mechanics, fluid dynamics, electromagnetics, and other fields of science and engineering.

Is FreeFem++ user-friendly for non-experts?

FreeFem++ has a user-friendly interface and provides a high-level language for describing PDEs and variational problems. However, some knowledge of finite element methods and programming may be required to use it effectively.

Can FreeFem++ handle complex geometries?

Yes, FreeFem++ can handle complex geometries by using unstructured meshes, which allow for more flexible and accurate discretization of the domain. It also has built-in tools for mesh generation and adaptation to handle complex geometries more efficiently.

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