# 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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### Given co-ordinates of 8 vertices, how to calculate the outward normal and surface area for each face of a irregular hexahedron?

I am working on an FEA mesh of hexahedron elements. The elemental level calculations involve finding the surface normals and area for each surface of a hex element. I preferred the vector cross ...
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### Gmsh for 3D volume with inclusions [closed]

In an attempt to create three-dimensional volumes with inclusions in Gmsh I stumble upon a problem which was non-existent in the two-dimensional case. I'm using the OpenCASCADE geometry kernel ...
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### Finite element convergence rate and possion's ratio

I am running simulations of a cantilever beam where it is fixed on one end and negative force applied to the other end. The first simulation is with 4-node linear quadrilateral elements and the other ...
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### Strain from FEM simulations to strain gauge measurements

I am looking for some intuition in making comparisons of FEM simulations to experimental measurements. In particular, I am interested in comparisons to strain gauge readings, and perhaps even LVDTs. ...
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### Is it possible to obtain a 'relaxing lengths' for 8 node hexaedral element

I am using 3D FEM with 8-node brick elements to model a certain type of growth/expansion, which is not a plastic deformation. First, I apply a pressure/load and I get displacement and the new position ...
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### Why do stabilized formulations for the Navier-Stokes equation maintain the convergence rate for high order polynomial interpolation?

I have a quick questions which has been troubling me lately. When reading the FENICS Finite Element Book they assess various approaches to solver the Stokes equation. Obviously, they discuss the ...
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### What is the difference between Abaqus and Calculix contact input?

I would like to say first that am new at using Calculix. I'm using Abaqus/CAE to create a cup deep drawing simulation and everything worked perfectly but my objective is to run the same exact ...
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### Penalization parameter for DG with jump penalization

I adapted this FEniCS code for my problem and I'm wondering if there is any good resource about how to choose the penalty parameter $\alpha$? Best case would be, if I can define it through some ...
121 views

### Taylor-Hood finite hexahedral elements, pressure diverging

I am developing a FEM fluid solver using the Taylor-Hood algorithm, i.e. quadratic interpolation for velocity, and linear for pressure. I have developed the code for 2-D quadrilaterals and triangles, ...
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### Prevent single node spikes in a FEM-simulation (using continuous Galerkin)

I am trying to solve a non-linear time-dependent heat equation $$\partial_tT=\nabla \left(k_T(T)\nabla T\right) + f$$ (similar to question Solving a non-linear heat equation with the galerkin method ...
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If $u_1$ and $u_2$ are solutions of (weak-form) Laplace equation on a connected domain $\Omega$, with Dirichlet boundary values $u_{\partial\Omega, 1}$ and $u_{\partial\Omega, 2}$, respectively. If $$... 1answer 102 views ### Compute outward normal and surface area for 8 noded brick element in FEA I have a cube which is divided into 8 small cubes by bisecting each edge, I am trying to find out the surface area of each of the faces and the corresponding outward normals for them. This operation ... 2answers 498 views ### Which SciPy nonlinear solver when Jacobian is analytically known and sparse? I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ... 1answer 66 views ### Stabilization parameter for an elliptic equation I simply want to solve the elliptic equation:$$ -\kappa \nabla^2 u + u = f $$where f\in [0,1]. When using continuous Galerkin with Lagrange elements, I have noticed that \kappa has to be greater ... 1answer 535 views ### Connectivity matrix in Finite Element Method in Triangular elements Imagine a simple triangular base mesh in finite element method with an unknown number of elements (varying by the user). How can connectivity matrix be coded to be generated automatically? 1answer 154 views ### Can a second-order ODE be “inconsistent” with its boundary conditions? I am trying to solve a set of coupled, nonlinear ODEs. The only dependent variable is a 1-dimensional spatial coordinate, let's call it x. For now, I've managed to approximate away some of the ... 1answer 158 views ### Does a generic method for solving a system of PDEs exist? There are generic methods for solving systems of ODEs numerically. Are there generic methods for PDEs? If so, what are they? If not, why not? To elaborate... Any set of ODEs can be written in ... 1answer 114 views ### How is nonlinear flux interface term assembled for Discontinuous Galerkin method for hyperbolic conservation laws? For example, for 1D Burgers equation$$ u u_x = 0 \\ $$equivalently,$$ \frac{dF(u)}{dx} = 0\\ F(u)= \frac{u^2}{2} If I want to obtain A_{ij},i\ne j for two DOFs (U_i and U_j) of two ... 0answers 40 views ### How to analyze the dispersion and dissipation of a certain FEM? In Finite Difference method or Finite volume textbook. Dispersion/Dissipation can be analyzed by set u = u_0\exp{\omega t +\mathbf{kx}}。 However, I cannot find something about this kind of analysis ... 1answer 271 views ### Why Coercivity is so important in FEM framework? I know Lax-Milgram theorem is fundamental to FEM. But it did not explain what will happen if coercivity is not met. My understanding is if it is met, eigen value of the operator (or its corresponding ... 3answers 667 views ### Why is the test function space in FEM chosen with homogeneous boundary conditions? It is so confusing, especially when I learns discontinuous galerkin method in broken Sobolev space and weak Dirichlet boundary condition. If the trial function is chosen with homogeneous boundary ... 0answers 61 views ### Should I expect computational gains using a second-order splitting method here? I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are: \begin{align} \nabla \cdot \vec{v} = 0, \tag{1} \\ \frac{\... 1answer 104 views ### A reference request for computational plasticity My background is in applied mathematics and I'm trying to learn plasticity. I have successfully understood the theory and finite element implementation of: linear elasticity, hyperelasticity (Neo-... 0answers 85 views ### Basic approach for numerical solution of PDE I'm looking for some guidance on how to write a program to numerically solve a PDE. As an example for comparison in 1D:\frac{d^2u}{dx^2} = f\;\;\;\;u(0) = 0\;\;\;\;u(1) = 0$$We could try 6 ... 2answers 114 views ### Analytical testing/quality control for scientific software in professional setting I am charged with maintaining a buildserver on Teamcity which is meant to test our in house FE software. Currently our test suite consists of a list of benchmarks which run every time a commit is made ... 1answer 54 views ### Oscillation term in a posteriori error estimator Assume that in the a (residual type) posteriori error estimator of some PDE is a term of the form h_T\|g\|_{L^2(\Omega)} involved where h_T is the diameter of an element and g is some known data ... 1answer 122 views ### Comparison between FEM and FDM methods for flow simulations What are the main differences between finite element and finite difference approach for incompressible flow simulations? I have a vague idea about how FE methods rely on minimizing the residual over ... 1answer 323 views ### Influence of node numbering in a FEM problem? In a FEM mesh, does the order of node numbering in an element has any importance? I'm currently trying to code my own FEM solver, which seems to work fine with quadrilateral elements, however I'm ... 0answers 224 views ### What is the mathematical and physical principle behind of RBE2 element？ I am writing a 3d linear finite element code to solve the standard linear elasticity equation on a tetrahedron mesh of a gearbox. Notice that, the two rectangular plates above the gearbox are fixed, ... 1answer 524 views ### How is rigid bodies implemented in finite element codes I am writing a finite element code for structural analysis, and I want to implement rigid bodies. How is this usually done? Say that I have a square mesh, with one half of the mesh being defined rigid ... 1answer 133 views ### Parallelization of FEM calculations I need to conduct some FEM calculations and I am wondering whether parallelization would be a good idea. The trouble is that my model is not especially large so it takes few seconds to solve a single ... 0answers 44 views ### Simplest meaningful PDE/FEM calculation for mechanical stress due to heat W have a complicated structure on which we do some FEM calculations regarding electrical potentials and heat distribution. The equations have the form \nabla\kappa\nabla u = f + g\rvert_{N} where ... 1answer 151 views ### Help debugging finite element solution in nonlinear elasticity I'm writing some code to solve problems in nonlinear elasticity using finite element methods. I have been following Bathe's book but I am having trouble with some nagging details. My question is ... 2answers 183 views ### Getting started with finite element modelling I'm a high-schooler building a small vehicle for an independent study. I've had finite element modelling recommended to me as a way to save time during the design process, and I'd like to try it out. ... 1answer 188 views ### How to simulate thermal expansion in a 2D plane using FEA? I am trying to model 2D thermal expansion of a square area inside another square using FEATool. I have simulated plane strain by incorporating forces pointing along the [1 \,\,\, -1]^T direction ... 0answers 177 views ### Getting started with FEM: Ill-conditioned matrix when evaluating flux terms in conservation law? I have a system of conservation laws of the form$$ \frac{\partial \mathbf{q}}{\partial t} + \nabla \cdot \mathbf{F}\!\left(\mathbf{q}\right) = 0 $$I want to use finite elements to solve this ... 2answers 473 views ### Unstructured mesh vs hybrid structured/unstructured for numerical simulations While answering one of the questions on meshing process, I encountered a lack of understanding on my end for the comparison of the mesh quality. First, consider an unstructured mesh created in GMSH ... 1answer 94 views ### How to implement Galerkin Method of Lines / FEM with black box integrators in scipy Suppose I have some time dependent PDE, which can be written in the strong form as$$ \frac{\partial u}{\partial t} + \mathcal{L}(u) = f $$Where \mathcal{L} is some differential operator. If I ... 1answer 109 views ### Reordering algorithm for minimization of ram usage of a skyline matrix The stiffness matrix of Ax=B system of linear equations, where A is an n\times n symmetric matrix stored in the form of symmetric skyline matrix, that is associated with a finite element model ... 1answer 104 views ### FEM-Laplace with Dirichlet in only a few points: Nonsingular operator? Let's consider the FEM discretization of the Laplace operator without boundary conditions, i.e.,$$ a(u,v) = \int_\Omega \nabla u \cdot \nabla v - \int_\Gamma (n\cdot \nabla u) v.  For one-...
Having shape functions $N_i(\xi,\eta), i = 1,...,N_n$ and, a normal vector $n = (n_x,n_y,n_z)$, a thickness function $F_\tau (\zeta), \tau = 1,...,N_\tau$ and nodal variables \$\mathbf{Q}_u = (Q_u,Q_v,...