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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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42 views

Determination of Jacobian when there are more than 1 degrees of freedom at a node

In finite element method, the formula for Jacobian is $ J =\beta^T X$ where, $\beta = [\frac{\partial N}{\partial \xi} \frac{\partial N}{\partial \eta}]$ and $X = [x_1 y_1; x_2 y_2; .. x_n y_n]$. ...
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40 views

Finite Element of Classical Plate Theory

I am trying to write a MATLAB program for solving a plate problem using Classical Plate Theory. I am using rectangular 4 noded element with 3 degrees of freedom on each node, $w$, $\frac{\partial w}{\...
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42 views

Discontinuous grids in finite element method

I am new to finite element and deal.ii library. I am using the finite element method for my research and going through the tutorials of deal.ii library. A deal.ii example has a grid generated like ...
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68 views

Normalization of polynomials for discontinuous Galerkin methods (DGM)

I was curious if someone could share their opinion on this matter. I have noticed that some people in literature normalize their Legendre polynomials, i.e. divide or multiply the polynomial by $$\...
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56 views

How to solve potential flow with FEM, stream function, and the Kutta condition?

I'm trying to solve two-dimensional potential flow over airfoils with the finite element method, using the stream function formulation ($\Delta\psi = 0$, $u = -\partial\psi/\partial y$, $v = \partial\...
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170 views

Size of jump for piecewise discontinuous approximations

If one has a sufficiently smooth function $u$ that is approximated by a piecewise constant function $u_h=\Pi^0_h u$ on a mesh of cell size $h$ (where $\Pi^0_h$ is the $L_2$ projection onto the ...
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1answer
71 views

Node renumbering in a 2D mesh

I have a 2D domain which is discretized using Q4 elements. I have the nodal positions and the element connectivity matrix. I would now like to renumber the nodes in such a way that all the interior ...
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89 views

Relation between conjugate gradient method and finite elements method

What is difference beetwen this two method? Are these methods far from each other or are these methods complement each other? Could you take an example?
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115 views

$H^1$-convergence rate of finite element method for Poisson equation, depending on element order

I wanted to verify my FEM-program by applying the method of manufactured solutions, while solving the Poisson equation in two dimensions using the continuous Galerkin method $$-\nabla^2u=f$$ with $$u=...
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34 views

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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74 views

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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46 views

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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42 views

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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30 views

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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49 views

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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82 views

Lower bound for bilinear form in FEM

I'm searching for lower bounds of bilinear forms arising in FEM for elliptic second order PDEs with mixed boundaries. I did some research and found: $$\max_{v_{h}\in\mathcal{V}_h(\mathcal{\Omega})}a(...
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28 views

FEM 1D poisson substitution integral issue

I'm trying to solve $ \begin{cases} -u''=f \\ u(0)=0 \\ u(1)= \alpha \end{cases} $ with FEM using reference elements and local coordinates. So we have the global ...
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2answers
113 views

Method to find PDE equation coefficient satisfying mean solution?

What is the best approach to go about solving a PDE problem of the type \begin{equation} k^3\Delta u - k(\mathbf{1}\cdot\nabla u) = 0\, ,\\ u=g\; \text{on}\; \Gamma_D\, ,\\ mean(u) = u_\text{...
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64 views

Element Preconditioner

Im just working on a preconditioner for the linear equation system $Ax = b$ arising in FEM for elliptic PDE. $A$ is a s.p.d Matrix with real valued entries. I read something about the element by ...
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2answers
122 views

Recommended visualization tools for higher order finite element solutions?

Is there any software available which can directly render higher order finite element results? In particular, 3D finite elements would be preferable. It seems gmsh has some capability in this regard ...
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28 views

Solving Compressible Euler in Primitive Variables with Galerkin P1 FEM

I have implemented a small compressible Euler solver, discretizing in primitive variables (rho, u, v, p) with standard Galerkin FEM P1 triangular elements, and mixed isotropic and anisotropic/...
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67 views

Relation of Condition of a Matrix and Convergency

Can anybody explain me the relation between the condition of a Matrix and the convergency of a problem. For example how is the relation between the condition of the stiffness Matrix occuring in FEM ...
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83 views

$L^2$ norm error estimates of conforming FEM about Poisson’s equation with mixed boundary conditions

Consider Poisson’s equation $$- \Delta u = f{\rm\qquad{ in }}\;\Omega $$ with following mixed boundary cconditions $$u = g{\rm\qquad{ on }}\;\Gamma \subset \partial \Omega $$ $$\frac{{\...
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1answer
138 views

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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1answer
84 views

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 ...
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2answers
77 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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1answer
102 views

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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1answer
85 views

seminorm of solutions of Laplace equation

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 $$...
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1answer
80 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 ...
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84 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 ...
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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 ...
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86 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?
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125 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 ...
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1answer
132 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 ...
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99 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 ...
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38 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 ...
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111 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 ...
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190 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 ...
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48 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{\...
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1answer
88 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-...
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80 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 ...
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2answers
105 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 ...
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1answer
51 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 ...
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1answer
140 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 ...
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89 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, ...
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143 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 ...
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1answer
107 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 ...
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39 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 $...
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1answer
103 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 ...
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28 views

CGFEM - Adding a solvent flux to a 1D adv-diff system as a source term

I have a system consisting of a narrow pipe with porous walls where the inlet conditions are flow rate and initial concentration, and the goal is to determine the change in concentration along the ...