Does anybody have experience with the Finite Difference Element Method described in http://www.scc.kit.edu/scc/docs/FDEM/Literatur/FDEM-Survey-Feb09.pdf and would advocate for or against using it? The method works on an unstructured grid, the field quantities are represented by their values at the grid points, and spatial derivatives are evaluated at the grid points by means of fitting polynomials into the gridpoints in the neightborhood of the respective gridpoint.
To me, at first sight, the method seems to have a couple of advantages, compared to FEM:
- The meaning of the state variables of the discretized system is intuitive
- It can be applied as a "black box" to virtually every PDE
- There is no a priori pen and paper work necessary for calculating weak forms, quadrature formulas etc.
- It can readily be extanded to rather high orders
- The PDE can contain arbitrarily high derivatives, in principle
- The error of the derivatives can be estimated
Does anyone know any drawbacks of the method?
The finite element method (FEM) is a numerical method for solving problems of engineering and mathematical physics. Typical problem areas of interest include structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The analytical solution of these problems generally require the solution to boundary value problems for partial differential equations. The finite element method formulation of the problem results in a system of algebraic equations. The method approximates the unknown function over the domain.[1] To solve the problem, it subdivides a large system into smaller, simpler parts that are called finite elements. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEM then uses variational methods from the calculus of variations to approximate a solution by minimizing an associated error function.
see more in https://en.wikipedia.org/wiki/Finite_element_method
Finite element method (FEM) is a powerful and popular numerical method on solving partial differential equations (PDEs), with flexibility in dealing with complex geometric domains and various boundary conditions. So it has a wide range of applications in Mechanical Engineering, Thermal and Fluid flows, Electromagnetic, Biomathematics, Geo Mechanics, etc.
Please refer the attachments for FEM
- Badges
- Science topic