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# Questions tagged [finite-element]

A means of solving ordinary and partial differential equations. The domain of the problem is broken up into elements, and the solution in each element is expanded in a basis of functions. The Finite Element Method lends itself well to adaptive refinement, irregular geometry, and good error estimates.

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### Gradient of field computed using FEM (L2 Projection)

From my understanding, in the finite element context, an L2 projection can be formulated as the following linear system: $$M\ \phi = \beta$$ where $M$ is the mass matrix, $\phi$ the resulting ...
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### Computational efficiency of Galerkin projection in AMG

I have been using recently AMG as preconditioner for CG with several meshes for simple elliptic problems discretised with linear elements on "complicated" three dimensional geometries and I ...
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### Computing Tangential Derivative using the Dirichlet value

Let $\Gamma$ be a smooth boundary of a domain $\Omega$. Let $u = g$ on $\Gamma$. How can I compute the tangential derivative of the function $u$ using the information that $u = g$ on $\Gamma$? Please ...
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### "Cleanest, most professional" approach to implement a finite differences scheme in dimension greater than two

Coding a finite difference algorithm in 1D does not require a complex mesh. In higher dimensions, you would need a mesh and its connectivity graph to compute the differential operators. Finite ...
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### Rolling friction settings in COMMERCIAL (Ansys) finite element software

Is there a standard way of implementing rolling friction in COMMERCIAL finite element software? There's no book about such a subject in COMMERCIAL FEM software though there are books on algorithms ...
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### Quintic Hermite shape functions

I am trying to use quintic Hermite basis functions for FEM applications, could someone please direct me to the general formula that would help me generate quintic Hermite shape functions? In natural ...
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### FEA with order reduced for a large system with a very localized force application

I have a large structure with many DOFs. But the application of force is very localized say over one or two nodes. If I try to run FEA on this with Guyan Reduction, I think the efficiency of reduction ...
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