# 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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### Determine Lagrange nodal variables of a simplex $T$

Consider a simplex $T$ in $R^d$ with $N_1(T) = \left\{N_i\right\}_{i=0}^{d}\subset P_1^{*}(T)$ be the Lagrange nodal variables (or nodal evaluation). By the Riesz representation theorem, there exist ...
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### stiffness matrix for 3D regular grid in FEM

I have understood the stiffness matrix for 3D truss, and programmed Ku=f from scratch (in Java) to find the displacements. Then I moved to 3D solid but lost in too many concepts and equations, such ...
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### Euler-Bernoulli beam element versus continuum beam element

I am using OpenSees to model a simply supported beam with a point load in the middle. The model is in consistent units. The beam is made up of bilinear quad elements. I have used 30 elements along the ...
I'm solving the Dirichlet problem for the Poisson equation in a 2d domain $D$: $$\begin{cases} \Delta u = 0 \quad \text{in D}, \\ u|_{\partial D} = u_0. \end{cases}$$ I'm interested in ...