# 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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### 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 ...
1 vote
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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?
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1 vote
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1 vote
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### If FEM is exact at the nodes, why do first and second-order elements give very different results?

I'm looking at the solution to a structural mechanics problem that is modeled with first-order elements and then as a comparison with second-order elements. It is clear that the first-order elements ...
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1 vote
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### Gmsh: what is the right syntax to iterate over a list of numbers with a For loop on the native language?

I'm new to Gmsh and after browsing many sites I haven't found the answer for this silly error. Using the native language of the software, I'm assigning a value to the Transfinite property of a bunch ...
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1 vote
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### How to incorporate a continuity of 1st derivatives at an internal interface in a 2nd order Poisson equation in finite elements method?

How should I modify the following matrix formulation of a finite element (FE) approximation of Poisson equation at the (internal) interface denoted by the nodes $i-1$ to $i+1$ having a continuous 1st ...
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### Decoupling Stokes problem into two problems: velocity and pressure, using FEM

I have seen finite difference methods for fluid equations (Stokes and Navier--Stokes) that solve a pressure problem first and then a fluid problem. That is, although they solve two different problems, ...
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It's well known that if we use 2nd order, centered, finite differences for the Laplace operator, we have that the matrix can be written as $$K=I \otimes A + A \otimes I$$ where $I$ is the identity ...