# 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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### RFEM: Equilibrium over plate section

I'm calculating a simple plate arrangement in RFEM: The plate has dimensions of 1m X 1m, thickness of 50mm. Elastic modulus of the material is 205000.0 N/mm2, Poisson's ratio is 0.3. The plate is ...
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### Projection (or fractional-step) methods Vs coupled method for incompressible Navier-Stokes

My question is in the context of the finite element method. Incompressible Navier-Stokes equations can be solved using the coupled method or projection/fractional step methods. Each method has its ...
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### General dimensional solution to fast sweeping quadratic equation

I am reading Hongkai Zhao's paper The Fast Sweeping method. I have implemented the method in 2D and now I want to move onto 3D. However section 2.6 confuses me. The article says: But I have no idea ...
290 views

### Under what circumstances is parallel scaling of the finite element method not "solved"?

I see things like this deal.II example, (ctrl + f for "superMUC") which seems to show some pretty impressive scaling (nearly twice as fast for twice as many CPU cores for a wide range of ...
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### Cohesive zone model finite element implementation

I have a 2D vector $\boldsymbol{u}$ and it's norm is $\lambda$. I have this function: $$\boldsymbol{T}=\dfrac{\boldsymbol{u}}{\lambda} e^\lambda$$ I need to compute $\boldsymbol{T}$ and it's Jacobean ...
1 vote
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### Accessing nodal and degree of freedom organisation in the solution vector in Fenics and Firedrake

Context Let suppose a solution to a finite element problem (associated to a mesh) stored in a vector $X$ of size $(N \cdot d)$ corresponding to $N$ nodes in the mesh and $d$ degrees of freedom for ...
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### RFEM: Tensile force in member in buckling analysis

Here is a simple T-shaped structure in RFEM. The structure is loaded from above, into the intersection of all members. I performed a buckling analysis, and obtained the buckling modes that I'm ...
1 vote
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### Evaluate the local mass matrix over a quadratic curvilinear tetrahedral element

I am evaluating the local mass matrix over a 3D curvilinear 10-node tetrahedral element. According to an index-naming rule, the shape functions are: \begin{equation} \begin{bmatrix} 2L^2_0 - L_0\\ ...
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### Schur complement formulation of linear system

Consider a system of the following form: $$(A+K)x=b$$ where $A$ is symmetric, positive definite and block diagonal (in fact, a block diagonal matrix made of stiffness matrices arising from FEM ...
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### Estimating forces on a model from the displacements of nodes

In any FEM problem involving mechanics, we try to solve the differential equation for the displacement field, $u$ given the force vector in the nodes, $F$. In industry, we often see our automobiles ...
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### Conceptual doubt regarding 2D conjugate heat transfer modelling (COMSOL and Mathemtica)

I have been dealing with some conceptual flaws in my understanding of modelling, which I will elaborate herein. I am modelling conjugate heat transfer of a reciprocating fluid, which flows with ...
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### books/paper recommendation on computational thermal-turbulence by using FEM

I have just learned basic FEM for 2D N-S euqation, now my teacher let me to do the following problem, the document of this problem is in large fluid problem, the system of equations is listed in that ...
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### Is it really necessary to solve a system of linear equations in the Finite Element Method?

When we solve some boundary value problem by Finite Element Method, the appropriate system of linear equations is built, $$Ax=b.$$ Usually we use the solution x just for plugging it into some ...
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### solve a coupled PDE system with some discontinuity by a mixed FEM

$$\begin{cases} u_t=f(u,v,\nabla{v}),\\ \Delta{[g(u)v]}=0. \end{cases}$$ I want to solve the above PDE system by a mixed FEM, that is, $u_t=f(u,v,\nabla{v})$ by discontinuous Galerkin (DG), where $f$...
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1 vote
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### FEM Basis for functions of two variables in $\mathbb{R}^2$ (Applied to Linear Full Stokes Equations)

I'm trying to do FEM for a very basic version of the linear full Stokes equations in two dimensions. Say we are working in the grid $[0,1]\times[0,1]$ in the $xy-$plane. To solve an FEM problem for a ...
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### time discretization via FEM to solve ODEs

It seems that FEMs are never seen to implement time discretization. Is time discretization via FEMs to solve ODEs ever possible?
1 vote
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1 vote
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### How do the current FEM opensource libraries compare?

Almost all FEM libraries are good enough, but I want to start with a FEM package and stick to it for some time. Instead of trying all of them, or going with what everyone else is using, I want to ...
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### Once a method is implemented in a computer program, then does learning the theory become less useful use of time?

Once a method is implemented in a computer program, then does learning the theory become less useful use of time? This has confused me. I used to view that all things should be studied from first ...
1 vote
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### Geometrically nonlinear finite element problem and mesh distortion

In my research on topology optimization of fluid-structure interaction problems (2D), I am using a geometrically nonlinear model to represent the structure. Body/surface forces are extracted from the ...