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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10
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3answers
747 views

Could you give examples of serious usage of meshfree methods?

I would like to hear about scientific codes and commercial packages utilizing meshless methods like Element-Free Galerkin based on Moving Least Squares functions. By "serious" I mean they could be ...
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1answer
656 views

Basic Finite Element Method (FEM) question: assembly and re-assembly

I'm reading up on the Finite Element Method (Zienkiewicz's Book), so I understand better what I'm doing in FEniCS and COMSOL. Currently, I'm wondering about this: Using FEM to solve fluid flow ...
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1answer
208 views

FETI-DP or BDDC with least squares FEM?

Have FETI-DP or BDDC methods been applied to alternative FEM discretizations - for example, least squares finite elements? My Google searching doesn't seem to yield many results, so I'm wondering if ...
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0answers
223 views

Choosing good basis functions to approximate a Lipschitz function

Let $D = \left\{0, t_1, t_2, \ldots, t_n\right\} \times [0,1]$ and $$ f: D\to [0,1], $$ be a function of time and a one-dimensional space. There is no analytical formula for $f$, but $f(t_i, \cdot)$ ...
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3answers
1k views

Capacitance in freefem++

I would like to simulate a capacitor in 2d with freefem++. This is the code I used: ...
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2answers
970 views

Feasibility and software for acoustic simulation

I'm looking at doing a finite-element simulation of air flow essentially for the purposes of approximating the response to an external audio impulse of a smallish (~10-30 cm scale), stationary 3D-...
4
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1answer
437 views

Slight mistake in Stochastic Galerkin code

I'm following Paul Constantine's Primer on Stochastic Galerkin Method, Section 3.1 (2D Poisson Example). In this matlab code, the example attempts to solve the PDE $$\alpha(w)(u_{xx}+u_{yy})=1 \text{ ...
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1answer
174 views

What is the most efficient way to represent a 1D function using $hp$-finite element basis functions

Given a one-dimensional function (let's say infinitely differentiable) and a prescribed accuracy of an L2 (or H1) norm, what is the optimal mesh and (in general arbitrary) polynomial orders on each ...
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1answer
165 views

What is the origin of the preasymptotic convergence behaviour in FEM?

When you have fine-scale features (e.g. boundary layers) in the solution, its FEM approximation on coarse meshes converge at strange apparent rates. Looking at Cea's lemma, is this behaviour because ...
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0answers
243 views

Negative viscosity stabilized by fourth order terms

I am trying to solve a "Navier-Stokes"-type problem where the viscosity is negative. Of course this renders the equation unstable and thus I add a fourth order term, so the entire equation becomes: $$...
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1answer
2k views

Abaqus *ORIENTATION

What do you actually type into the *ORIENTATION entry in an input file? Is it a rotation matrix w.r.t. the Global axes?
4
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1answer
248 views

How can exponential fitting be used with the finite element method?

Restricted to one dimensional problem, is it possible to dynamically adapt the finite element method (FEM) discretisation based on the local value of the Péclet number ($P_e$) for advection-diffusion ...
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2answers
3k views

Does the finite element method impose any restrictions on the Peclet number for numerical stability?

Background on finite volume method When discretising the flux with a central difference stencil of the the advection-diffusion equation restriction $\frac{ah}{d} < 2$ must be observed for the ...
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1answer
254 views

Proving convergence of adaptive finite elements - min res FEM?

There's a body of work out there dealing with the discrete convergence of adaptive finite element methods using error estimators. Most deal with proving the property $\|u-u_{k+1}\|_U \leq (1-\alpha) \...
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3answers
537 views

Are there finite element software who handles more than five dimensions?

I'm a beginner with FE. My application is the pricing of financial derivatives where the space is five dimensional. So, adding time, the problem has six dimensions. I tried to look around (Fenics, ...
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1answer
1k views

boundary conditions for electrostatic problem

I'm solving an electrostatic problem governed by Laplace equation $$-\nabla \cdot (\rho^{-1} \nabla u) = 0$$ in the following domain: a brick ($\Omega_1$) with a cylindrical inclusion ($\Omega_2$), ...
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3answers
595 views

A problem in 1D linear finite element method

When applying Galerkin method, we have two conventions, i.e. multiply the test function $v$ at left/right, $(v,u)/(u,v)$. Both ways won't matter for a simple problem like Poisson's equation, since the ...
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3answers
1k views

Significance of p-convergence studies

Consider a method (e.g., FEM) with variable approximation order $p$. Now, we know that the optimal order of convergence is given by $$e = C h^{p+1},$$ where $h$ denotes the mesh size and a constant $C$...
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0answers
85 views

References on the topic of DEM and XDEM

DEM: discrete element method. XDEM: extended discrete element method. For my current project of furnace simulation with granular materials, I am interested in the methods mentioned above. I have not ...
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3answers
315 views

Pseudo-inverse of a discretized operator with a null space?

Is there a way to understand what happens when a singular operator is discretized and inverted using the pseudoinverse (say using the SVD Moore-Penrose pseudoinverse)? For example, if we discretize ...
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3answers
1k views

approximating normal derivative of a continuous function with shape functions

This is probably a very trivial question but I have not been able to figure it out myself, so here goes. Let $\Gamma$ be a smooth boundary in 2-D divided into $N$ quadratic (3-noded), continuous, ...
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1answer
3k views

Stress due to the mismatch of thermal expansion coefficients of two different attached materials in COMSOL

I'm simulating the thermo-electro-mechanical behavior of a copper wire which is surrounded by silicon dioxide. In other words, the wire segments is under mechanical and thermal loads and at the same ...
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3answers
938 views

Conforming mesh refinement for quads/hex elements

The context - I'm working with a spectral FE (higher order interpolation at GLL nodes) code on conforming hexahedral meshes, and our PI is interested in improving mesh quality, possibly with adaptive ...
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3answers
35k views

What are the conceptual differences between the finite element and finite volume method?

There is an obvious difference between finite difference and the finite volume method (moving from point definition of the equations to integral averages over cells). But I find FEM and FVM to be very ...
6
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2answers
833 views

Local inversion of small matrices on GPUs?

I don't know much about GPU computing at the moment, so please pardon the simple question. Can one invert local matrices in parallel on the GPU? CUBLAS doesn't seem to support factorization, and most ...
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2answers
717 views

Evaluation of Vandermonde matrix

I would like to construct a Finite Element basis by using a generalized Vandermonde matrix. The idea is to compute the values of a suitable modal basis ('prime basis') at a set of points in reference ...
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2answers
2k views

Finite elements for Stokes with traction boundary conditions

Suppose we are given the Stokes equations with Neumann conditions on part of the boundary: $-\nabla\cdot\boldsymbol{\sigma} = \mathbf{f}, \quad \text{and} \quad \nabla\cdot \mathbf{u} = 0 \quad \...
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1answer
669 views

metis partitioning for structured multi-block grids

Metis is purpose-built for partitioning graphs and unstructured meshes one uses in finite element/volume methods, and it works great for this. I have a 3D structured multi-block topology, where each $...
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1answer
204 views

What Linear Equation Solver should be used for a problem with many dirichlet conditions?

I am solving a laplace equation on a finite-element mesh (tetrahedral, triagonal) and have many say 99% dirichlet conditions compared to the number of unknowns. Is there an efficient way to solve this ...
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263 views

Curvature of level-sets of CG1 function

Let us have simplicial mesh and continuous function $u$ which is piece-wise linear and non-constant on every cell. Then normal vector to level-sets of $u$ is given $$\mathbf{n}=\frac{\nabla u}{|\nabla ...
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1answer
1k views

weak formulation of coupled pdes for fenics

I am trying to implement the following system of time-dependent, coupled nonlinear pdes in FEniCS: $$\partial_{t}\rho+2\left(\nabla\rho\nabla\phi+\rho\nabla^{2}\phi\right)+2\sigma\rho\left(\rho-1\...
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2answers
852 views

Need an example of convection-dominated problem to test on FreeFEM++

Can you all give me (at least) one example about convection-dominated problem in order that I can test it (them) on FreeFEM++. If possible, please give me specific examples (it/they contain(s) full ...
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3answers
5k views

What is the purpose of using integration by parts in deriving a weak form for FEM discretization?

When going from the strong form of a PDE to the FEM form it seems one should always do this by first stating the variational form. To do this you multiply the strong form by an element in some (...
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1answer
1k views

defining subdomains in FEniCS (Python) using obtained (solved) variable [closed]

I'd very much appreciate if you could help me out with this as I think I'm missing something simple out or should be using alternate syntax: I am running the following Python code in FEniCS, where I ...
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2answers
690 views

What is the basic requirement to understand the PETSc library?

I want to use the PETSc library to do some numerical work on finite element and parallel computing, but I wonder what I should know first to use these libraries. Could you give me some guiding ...
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2answers
109 views

Quantification of non-stationarity of PDE solution

Suppose I have a time-dependent PDE discretized by the Rothe method and FEM, like $$ \int_{\Omega} k^{n+1/2}(u^{n+1}-u^{n}) v \;\mathrm{d}x = F^{n+1/2}(u^{n+1},u^n)[v] \quad \forall v\in V_h^n. $$ ...
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1answer
325 views

A simple question about 1D finite element derivatives

For 1D derivative we have \begin{equation} F(x) = \frac{\partial f(x)}{\partial x} \end{equation} \begin{equation} f(x)=\sum_{i}f_ie_i(x) \end{equation} \begin{equation} F(x)...
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3answers
8k views

What is the difference between implicit FEM and explicit FEM?

What is the difference between explicit FEM and implicit FEM exactly? According to the post here, it seems that the only difference is whether implicit or explicit time integration is used. As I ...
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3answers
1k views

Best Methodologies for Managing a Mesh in Parallel Finite Element Computation?

I am currently developing a domain decomposition method for the solution of the scattering problem. Basically I am solving a system of Helmholtz BVPs iteratively. I discretize the equations using ...
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1answer
543 views

Implementation of a contraction force in Fenics

Is there any way to implement an element wise contraction force (i.e., a force which causes the FEs themselves to contract onto themselves)? For example this would happen when something dehydrates. ...
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2answers
2k views

FEniCS: importing mesh along with material and boundary data

Which is the preferred way to import into a FEniCS (python) program a mesh which was generated in an external generator which provides sub-domain and boundary markers? I was using MeshData->...
4
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1answer
141 views

Assembling FE tensors using different quadrature degrees

Assume we have few terms contributing to element tensor and each requires different quadrature degree to be integrated exactly. Does it generally worth using different quadrature degrees for each term ...
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2answers
975 views

Flux across a non-boundary line segment in FEniCS

I am solving an elliptic boundary value problem on a subset of the rectangle [-1,1]x[-1,1]. The domain contains the line segment x=0, however this does not need to be a part of the boundary, so it is ...
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2answers
2k views

FeniCS: Visualizing high order elements

I've just started messing around with FEniCS. I am solving Poisson with 3rd order elements and would like to visualize the results. However, when I use plot(u), the visualization is just a linear ...
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2answers
1k views

How can I build a mesh with holes for use in FEniCS?

This is my first time using FEniCS. I am trying to solve an elliptic PDE, fairly similar to the Laplace equation, on a rectangle with two holes in it. The holes are level sets of an energy function, ...
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2answers
3k views

Discontinuous Galerkin / Poisson / Fenics

I am trying to solve the 2D Poisson equation using the Discontinuous Galerkin method (DG) and the following discretization (I have a png file but I am not allowed to upload it, sorry): Equation : $$\...
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2answers
4k views

Open-source 3D FEM Solver for Electromagnetics (Time-Harmonic Maxwell)

I was wondering if there exist any good (accurate/fast/easy-to-use) open-source FEM solvers for 3D time-harmonic Maxwell's equations. I am looking to simulate systems a few wavelengths large in the X/...
6
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1answer
821 views

FEniCS: how to access coordinates when writing an equation for a trial function

I need to solve the following equation in FEniCS: $$ \boldsymbol{\nabla} \cdot \begin{pmatrix} f(y)\frac{\partial u}{\partial x} - g(x,y)\frac{\partial u}{\partial y} \\ - g(x,y)\frac{\partial u}{\...
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1answer
515 views

Fenics: time-independent Sine-Gordon equation

Is there a code for the equation $$ \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2} = \sin(u) $$ or for the sine gordon equation in two dimensions because I want to change some ...
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0answers
740 views

How to apply periodic boundary conditions to a Raviart-Thomas finite element space in Fenics? [closed]

I'm trying to use periodic boundary conditions within a Raviart-Thomas finite element space in Fenics (dolfin 1.2.0) in a Ubuntu 12.04 (amd64) machine (with python 2.7). If other FE space is used, ...