We’re rewarding the question askers & reputations are being recalculated! Read more.

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.

Filter by
Sorted by
Tagged with
1
vote
2answers
132 views

Lattice Boltzmann methods vs Navier stokes/ other eulerian methods for *water* simulation

Note, there is already a question here, however the answers don't answer the original question, let alone specific considerations when dealing with nearly in-compressible fluids (water). Another ...
2
votes
0answers
49 views

What is appropriate boundary condition for Poisson pressure equation?

I'm doing CFD simulations in unstructured grids. Well, it's a bit different from conventional unstructured grids that are used mainly in FEM or FVM as tetrahedral meshes. Mine is a voxelized mesh of ...
0
votes
1answer
37 views

Can we use interpolation function of different order to represent different degrees of freedom in a FEM element?

Consider a line element in FEM. Let each node have 3 DOF. They are x and y translation DOF and temperature. Can we use interpolation functions of different orders for the translation DOFs and ...
0
votes
0answers
12 views

Efficient Alternatives to Operator Splitting in NLSE

Lately i've been trying to decide my thesis theme and i've become interested in adaptive finite elements and finite volumes algorithms. However, I need my thesis to fit into a physics related theme. ...
2
votes
0answers
67 views

Extracting FEM matrices in matlab pde toolbox

I am trying to follow the dynamic linear elasticity in Matlab, link here. My goal is to extract the FE Matrices using the function assembleFEMatrices in matlab and solve the resulting system of second-...
2
votes
1answer
227 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 ...
1
vote
0answers
27 views

Setting up diffusion with integral B.C. in Fenics

I'm trying to model diffusion through a cylindrical domain $D = \{ (x,y,z) : x^2 + y^2 \leq 1, \;\; 0 \leq z \leq 1\}$. The is an initial concentration of the diffusant at the upper flat surface, ...
0
votes
0answers
28 views

Divergence issues when using intrinsic cohesive elements approach

When I model the strain localisation of a microscopic sample (or say RVE ) with cohesive elements approach, the convergence performance looks very terrible. I have to use extremely time increments (...
1
vote
1answer
77 views

Fenics: solving the same PDE multiple times

I am new to Fenics and just started reading the tutorial Solving PDEs in Python. For simplicity, we can refer to simplest example, page 17 (the linear poisson equation), despite not necessary. My ...
1
vote
0answers
39 views

Finite element lemma proof

I was curious if anyone could help or provide a reference for the proof to the following lemma Lemma: Let $P_{1}$ be the set of polynomials of the first degree and let $W = w(x) : w \in C([0,1]), ...
1
vote
2answers
45 views

Evaluation of slope at iteration ith - Newton-Raphson method

I'd like to know how Ansys computes the slope (=stiffness matrix) at point x1 in figure. I'm studying the way in which Ansys uses the Newton-Raphson method when there are nonlinearities. In the slide ...
0
votes
1answer
106 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 $$...
3
votes
1answer
52 views

Weighted QR Implementation

Say I want a QR decomposition of matrix $A$, where orthogonality of $Q$ is with respect to a generic non-degenerate positive-definite bilinear form $\phi$ (in my case, $\phi$ is "defined" by a finite-...
6
votes
3answers
9k views

The real myth of GPU (specifically CUDA) really speed up FEM/CFD

Now I have been believing that FEM/CFD is supposed to be faster on a GPU unit - here I am using CUDA as solid example. However, I have not been able to find a convincing paper where the benchmark ...
1
vote
0answers
25 views

Finite difference/element method : time step and spatial resolution close to a finite singularity

I'm using the finite element method (FEM), but my question is quite a global question. It's related to this question but it is not the same. Let's assume we have this equation : $$\partial_t c - u\...
3
votes
0answers
80 views

numerical instabilities in Fluid Dynamics, Finite Element Method

I'm looking for references to understand where the numerical instabilities come from in hydrodynamics in general, and notably when the Péclet number: $Pe>1$. I'm using the finite element method. ...
1
vote
0answers
51 views

Derivatives over a Finite Element mesh

I have a data extracted from Comsol on some node points and I know the coordinates of each node. Does anyone know how Comsol calculate the partial derivative from the values at each node and also ...
0
votes
0answers
37 views

FEniCS implementation of Maxwell equations for a dipole antenna

someone knows where I can find a FEniCS implementation of Maxwell equations for a dipole or other type of antenna? I mean a dipole antenna with an arbitrary geometry of every 'leg' in the dipole.
3
votes
1answer
127 views

Why do many people use FDM method to solve Stokes equations, i.e., saddle point matrix?

For numerical methods of the Stokes equations, with appropriate boundary: $$-\nabla^{2} \vec{u}+\nabla p=\overrightarrow{0}$$ $$\nabla \cdot \vec{u}=0$$ one may use FDM (finite difference method) ...
1
vote
1answer
148 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(...
0
votes
0answers
19 views

Inconsistent potential over a cylindrical surface in COMSOL

I made the following construction in COMSOL (This is a cut): Two cylinders, the inner one in the middle is a solid cylindrical conductor. The thick outer cylindrical shell, along with the two small ...
0
votes
2answers
314 views

Imposing total pressure over surface in FEM

I am trying to solve Stokes problem using Finite element method. My question is how to impose that total pressure over the surface is zero to remove the constant pressure mode?
0
votes
0answers
64 views

How to implement the following Finite Element method for Burgers' equation?

I am trying to replicate this result. It involves using the Galerkin finite element approach onto the viscous Burgers' equation. However, my implementation (in R) seems to be giving me wrong results....
0
votes
1answer
54 views

Determination of Young's Modulus for a Finite Element Code

I am writing a finite element code for my final year project of BS Mechanical Engineering. The geometry is an integration of several parts composed of different materials. I don't have exact values of ...
0
votes
1answer
41 views

How to define $P0-$ Piecewise constant basis function in finite element method?

Suppose if we take $X_h(G)$ as finite element space then this space (space of piecewise constant basis function)is defined as $$X_h=\{v: v|_{T}=c_{T}, T \in \mathbb{T}\},$$ where $\mathbb{T}$ is a ...
10
votes
1answer
346 views

DG local equation, how to interpret mean-averaged test function

In the paper http://www.sciencedirect.com/science/article/pii/S0045782509003521, an HDG element-local equation is described on page 584 equation (4), with one of the equations taking the following ...
0
votes
0answers
40 views

Cubature rule in unit Sphere in $\mathbb{R}^{3}$

I need to find the cubature rule for the following integration $$\int_{S^{2}} f(s,\tilde{s})d\tilde{s} ds,$$ where $S^2$ is the unit sphere in $\mathbb{R}^{3}$.
1
vote
1answer
219 views

(FEM) Nodes reordering for sparse matrix storing techniques

Is it necessary to reorder nodes (using Reverse Cuthill-Mckee algorithm, for example) if I am already using a CSR or CSC storing technique? Because since CSR/CSC stores only non-zero elements I guess ...
3
votes
1answer
83 views

Reference request: Riks method (Nonlinear FEM)

I'm struggling to find a good detailed reference explaining the Arc-length method or, more generally, Riks method and its derivations. I looked for the classical books in nonlinear mechanics (the ones ...
0
votes
2answers
260 views

Boundary conditions for streamlines in enclosed flow

I am trying to solve Lid driven square cavity flow problem of Stokes equation using finite element method. I have boundary conditions for velocity as zeros on every boundary but u=1 on top boundary. ...
0
votes
1answer
129 views

Finite Element - Flux Calculation

I am solving an advection-diffusion equation using the FEM and am having trouble calculating my fluxes. I start with the equation, $$\frac{\partial n}{\partial t} = \frac{\partial j_{n}}{\partial x}\...
7
votes
1answer
533 views

Time discretization of the variational formulation of the Navier-Stokes equation

I've asked this question on mathoverflow too. Let $T>0$ $I:=(0,T]$ $d\in\mathbb N$ $\Lambda\subseteq\mathbb R^d$ be nonempty and open, $$\mathcal V:=\left\{\phi\in C_c^\infty(\Lambda,\mathbb R^d):...
0
votes
1answer
179 views

Proving solution existence and uniqueness of the Helmholtz equation with Robin boundary conditions with complex coefficients

I am trying to solve the Helmholtz equation with Robin boundary conditions with complex coefficients and the weak formulation $$ \iint_\limits\Omega\nabla p_0(x,y)\nabla\left(\overline{v(x,y)}\right)...
2
votes
1answer
152 views

Non-linear flux interface condition - variational formulation

Context: I am working on implementing this paper and I am struggling to come up with a variational formulation for the Butler-Volmer interface conditions. To simplify my question I consider the ...
1
vote
1answer
83 views

Iterative solution of ill-conditioned matrix systems

I want to solve a matrix system of the form $Ax=b$ where $A$ is ill-conditioned. The matrix system comes from a structural simulation problem which was discretized using finite elements. I do not have ...
4
votes
3answers
598 views

Pre/Post-processor for an academic finite element solver

I'm currently developing a finite element solver for academic/research purposes. Therefore I'm searching for a pre- and postprocessor in my toolchain. For a previous project I have used gmsh as a ...
5
votes
1answer
101 views

Approximate $\|\Delta f\|^2_{L^2(\Omega)}$ in finite element context

I have minimization problem of the form $$ G(f) + \|\Delta f\|^2_{L^2(\Omega)} \to \min $$ over all $f\in C^2(\Omega)$, $\Omega$ being closed and bounded. Let us forgot about $G$; I'm interested in ...
0
votes
1answer
463 views

Finite Element Analysis for Laminated Plates with Holes or Patches

As the title says, I am trying to code in FEM a plate structure that either has a hole in one of the layers or one of the layers is made of patches of plates, rather than one whole plate. However, ...
0
votes
2answers
330 views

(FEM) 1D time-dependent heat equation convergence problem

I'm simulating a simple 3-node bar with convection BCs at the edges to validate my FEM code. The following data was used: Initial temperature = 25 ºC Temperature surrounding the rod = 10 ºC Thermal ...
3
votes
1answer
74 views

Good reference on the implementation and limitations of SDIRK methods

For the solution of many PDE, implicit high-order time integration schemes are required. I am specifically interested in schemes that do not require a constant time step. I am well acquainted with ...
1
vote
0answers
16 views

Equi-order in pressure correction schme of Navier-Stokes equation

I am wondering if there is an stabilized equi-order scheme in pressure correction scheme in solving Navier-Stokes equation? Usually P2-P1 element combination is used to solve NS equation, and a PSPG ...
0
votes
0answers
23 views

Automatic single point constraint

A lot of modern FE codes have an option called AUTOSPC. Examples are Nastran or Marc. I know that this option removes degrees of freedom to avoid a singular matrix system. But how to determine ...
2
votes
1answer
126 views

How to use Newton-Raphson method to handle nonlinear terms in coupled system of PDEs?

I'm trying to solve the Nonlinear Schrodinger's Equation (NLSE) in 2D using Finite Elements, but I don't know how to handle the nonlinear term. I suppose I have to apply the Newton-Raphson algortihm ...
0
votes
0answers
61 views

Shape functions in Euler Bernoulli Beam Equation

Does anyone have a intuitive explanation of why Hermite polynomials have to be utilized as the shape functions in the FEM solution of the Euler Bernoulli Beam 4th order ODE? I have been learning FEM ...
8
votes
1answer
175 views

Should we always expect FEM error plots to be straight lines?

The error estimates in FEM are usually of the form $$||u^h-u||\leq Ch.$$ Taking logarithm on both sides, we obtain $$\log ||u^h-u||\leq \log C + \log h.$$ This estimate implies that the error lies ...
3
votes
0answers
52 views

Strain propagation from surface to bulk in COMSOL

I am trying to simulate strain propagation from the surface into the bulk. I have a rectangular semiconductor block (~2 μm thick) on top of which metal gates (~25 nm thick) are deposited as seen in ...
2
votes
0answers
41 views

References to solve system of differential equations which describe the evolution of sandpile surface using the finite element method

I want to solve the following nonlinear system in 1D \begin{cases} \dot{R} + v \frac{\partial R }{\partial x} - \frac{\partial }{\partial x}\left( D \frac{\partial R }{\partial x} \right) -\Gamma =...
4
votes
1answer
93 views

Original paper on the augmented Lagrangian method in FEM

I am writing a paper in which I want to cite the earliest reference to the augmented Lagrangian method in FEM. For the pure Lagrangian method in FEM, the classical work of Babuška [1] is the original ...
1
vote
2answers
164 views

Order of element vs Degrees of freedom of the element

I have read that the order of the element is the order of the polynomial used to approximate/represent the field variable in that element. If we consider a one-dimensional, 2 degrees of freedom ...
4
votes
1answer
258 views

Interpolating a mathematical function using a Hermite Cubic Finite Element Space

I have a Hermite Cubic Finite Element Space on a computer in the form of Matlab m-files. More specifically, I can evaluate four "shape functions" $N_1, N_2, N_3,$ and $N_4$, for which the following ...