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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0answers
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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0answers
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 $$\...
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0answers
56 views
How to solve potential flow with FEM, stream function, and the Kutta condition?
I'm trying to solve two-dimensional potential flow over airfoils with
the finite element method, using the stream function formulation
($\Delta\psi = 0$, $u = -\partial\psi/\partial y$, $v =
\partial\...
7
votes
1answer
170 views
Size of jump for piecewise discontinuous approximations
If one has a sufficiently smooth function $u$ that is approximated by a piecewise constant function $u_h=\Pi^0_h u$ on a mesh of cell size $h$ (where $\Pi^0_h$ is the $L_2$ projection onto the ...
1
vote
1answer
71 views
Node renumbering in a 2D mesh
I have a 2D domain which is discretized using Q4 elements. I have the nodal positions and the element connectivity matrix. I would now like to renumber the nodes in such a way that all the interior ...
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1answer
89 views
Relation between conjugate gradient method and finite elements method
What is difference beetwen this two method? Are these methods far from each other or are these methods complement each other? Could you take an example?
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3answers
115 views
$H^1$-convergence rate of finite element method for Poisson equation, depending on element order
I wanted to verify my FEM-program by applying the method of manufactured solutions, while solving the Poisson equation in two dimensions using the continuous Galerkin method
$$-\nabla^2u=f$$
with
$$u=...
0
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1answer
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 ...
3
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0answers
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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1answer
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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1answer
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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0answers
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 ...
2
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0answers
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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0answers
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:
$$\max_{v_{h}\in\mathcal{V}_h(\mathcal{\Omega})}a(...
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votes
1answer
28 views
FEM 1D poisson substitution integral issue
I'm trying to solve
$
\begin{cases}
-u''=f \\
u(0)=0 \\
u(1)= \alpha
\end{cases}
$
with FEM using reference elements and local coordinates.
So we have the global ...
1
vote
2answers
113 views
Method to find PDE equation coefficient satisfying mean solution?
What is the best approach to go about solving a PDE problem of the type
\begin{equation}
k^3\Delta u - k(\mathbf{1}\cdot\nabla u) = 0\, ,\\
u=g\; \text{on}\; \Gamma_D\, ,\\
mean(u) = u_\text{...
3
votes
0answers
64 views
Element Preconditioner
Im just working on a preconditioner for the linear equation system $Ax = b$ arising in FEM for elliptic PDE. $A$ is a s.p.d Matrix with real valued entries. I read something about the element by ...
3
votes
2answers
122 views
Recommended visualization tools for higher order finite element solutions?
Is there any software available which can directly render higher order finite element results? In particular, 3D finite elements would be preferable. It seems gmsh has some capability in this regard ...
2
votes
0answers
28 views
Solving Compressible Euler in Primitive Variables with Galerkin P1 FEM
I have implemented a small compressible Euler solver, discretizing in primitive variables (rho, u, v, p) with standard Galerkin FEM P1 triangular elements, and mixed isotropic and anisotropic/...
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1answer
67 views
Relation of Condition of a Matrix and Convergency
Can anybody explain me the relation between the condition of a Matrix and the convergency of a problem.
For example how is the relation between the condition of the stiffness Matrix occuring in FEM ...
3
votes
0answers
83 views
$L^2$ norm error estimates of conforming FEM about Poisson’s equation with mixed boundary conditions
Consider Poisson’s equation
$$- \Delta u = f{\rm\qquad{ in }}\;\Omega $$
with following mixed boundary cconditions
$$u = g{\rm\qquad{ on }}\;\Gamma \subset \partial \Omega $$
$$\frac{{\...
1
vote
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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votes
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, ...
2
votes
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 ...
-1
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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 $$...
-1
votes
1answer
80 views
Compute outward normal and surface area for 8 noded brick element in FEA
I have a cube which is divided into 8 small cubes by bisecting each edge, I am trying to find out the surface area of each of the faces and the corresponding outward normals for them. This operation ...
2
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0answers
84 views
Which SciPy nonlinear solver when Jacobian is analytically known and sparse?
I have a nonlinear function fun with n inputs and n outputs. I also have a function jac which calculates the Jacobian, which is ...
4
votes
1answer
66 views
Stabilization parameter for an elliptic equation
I simply want to solve the elliptic equation:
$$
-\kappa \nabla^2 u + u = f
$$
where $f\in [0,1]$. When using continuous Galerkin with Lagrange elements, I have noticed that $\kappa$ has to be greater ...
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1answer
86 views
Connectivity matrix in Finite Element Method in Triangular elements
Imagine a simple triangular base mesh in finite element method with an unknown number of elements (varying by the user). How can connectivity matrix be coded to be generated automatically?
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vote
1answer
125 views
Can a second-order ODE be “inconsistent” with its boundary conditions?
I am trying to solve a set of coupled, nonlinear ODEs. The only dependent variable is a 1-dimensional spatial coordinate, let's call it $x$. For now, I've managed to approximate away some of the ...
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vote
1answer
132 views
Does a generic method for solving a system of PDEs exist?
There are generic methods for solving systems of ODEs numerically. Are there generic methods for PDEs? If so, what are they? If not, why not? To elaborate...
Any set of ODEs can be written in ...
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vote
1answer
99 views
How is nonlinear flux interface term assembled for Discontinuous Galerkin method for hyperbolic conservation laws?
For example, for 1D Burgers equation
$$
u u_x = 0 \\
$$
equivalently,
$$
\frac{dF(u)}{dx} = 0\\
F(u)= \frac{u^2}{2}
$$
If I want to obtain $A_{ij},i\ne j$ for two DOFs ($U_i$ and $U_j$) of two ...
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0answers
38 views
How to analyze the dispersion and dissipation of a certain FEM?
In Finite Difference method or Finite volume textbook. Dispersion/Dissipation can be analyzed by set $u = u_0\exp{\omega t +\mathbf{kx}}$。
However, I cannot find something about this kind of analysis ...
3
votes
1answer
111 views
Why Coercivity is so important in FEM framework?
I know Lax-Milgram theorem is fundamental to FEM. But it did not explain what will happen if coercivity is not met.
My understanding is if it is met, eigen value of the operator (or its corresponding ...
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3answers
190 views
Why is the test function space in FEM chosen with homogeneous boundary conditions?
It is so confusing, especially when I learns discontinuous galerkin method in broken Sobolev space and weak Dirichlet boundary condition.
If the trial function is chosen with homogeneous boundary ...
3
votes
0answers
48 views
Should I expect computational gains using a second-order splitting method here?
I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are:
\begin{align}
\nabla \cdot \vec{v} = 0, \tag{1} \\
\frac{\...
1
vote
1answer
88 views
A reference request for computational plasticity
My background is in applied mathematics and I'm trying to learn plasticity. I have successfully understood the theory and finite element implementation of: linear elasticity, hyperelasticity (Neo-...
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0answers
80 views
Basic approach for numerical solution of PDE
I'm looking for some guidance on how to write a program to numerically solve a PDE. As an example for comparison in 1D:
$$\frac{d^2u}{dx^2} = f\;\;\;\;u(0) = 0\;\;\;\;u(1) = 0$$
We could try 6 ...
4
votes
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 ...
2
votes
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 ...
2
votes
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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0answers
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, ...
5
votes
1answer
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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votes
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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0answers
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 $...
2
votes
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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0answers
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 ...
