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 ...

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27 views

Produce large displacement under small displacement approximation?

I have managed to make my model converge fairly well and achieve large displacements and deformations. It exhibits stress and strain good continuity by solving it under small displacement and ...
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55 views

Open source FEM implementation for Windows

I am wondering is there any robust, well-tested, accurate open source FEM solver package for Windows? I would like to use to power the engine of my structural engineering application. The FEM package ...
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0answers
22 views

Relaxation Parameters for Steady Navier-Stokes

I am working on a project involving steady solutions for the Navier-Stokes Equations. In the past I've only worked with the unsteady Navier-Stokes, so some of this is new to me. In particular, at ...
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0answers
41 views

Basis over edges of a mesh

In 2D, the hat functions are the usual function basis for the finite dimentional space $\{v\in \mathcal{C}:v|_T\in P_1(T)\,\forall T\}$: set of continuously functions that are polynomials less than or ...
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21 views

One domain subdivided in many subdomains to be refined independently

I have a domain divided in several subdomains (for example: 10000 subdomains), and solve an independent problem on each subdomain through some finite element method (then I assemble each solution on a ...
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36 views

Mesh partitioner with user-defined overlap

I am looking for a mesh partitioner, where I can specify overlap, for example h = 3. I have looked into metis, but I wasn't able to find such a functionality. Is there any other package which ...
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2answers
78 views

How does rigid body rotation affect resuts in a simulation?

I have been running a finite-element simulation where, for the sake of convergence, I chose to stay in small deformation hypothesis (in comsol, include non-linear geometry box not checked for who that ...
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1answer
79 views

Two-dimensional mesh in fem: generating P1, P2, P3,… mesh from a P1 mesh

I have a two-dimensional mesh generated by triangle (the mesh generator software is not relevant). This software generates a perfect mesh for approximate the solution by piecewice linear functions (P1 ...
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46 views

Meaning of this minimal python and FEniCS based wave propagation code? [closed]

This is a question about understanding a piece of random code that does not necessarily require knowledge of it's theory. This is very specific and may not be of use to the community in general but ...
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1answer
116 views

Understanding Finite-Element Modal Analysis

I am teaching a basic course on computational physics and for the last part of the course I will introduce freshman physics undergraduates to finite-element modelling methods. I am preparing a ...
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40 views

Spectral/hp-finite elements for 4th order PDEs

Does anyone know of references discussing the solution of 4th order PDEs by way of spectral/hp-finite element methods? Specifically, I'm interested in the extension of the spectral element method, ...
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28 views

FEM libraries with trace spaces

To implement hybridizable discontinuous Galerkin methods, one needs finite element spaces defined on the skeleton of the mesh. deal.II has support for HDG through FE_FaceQ class which provides ...
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63 views

Mass Lumping in case of Dirichlet boundary conditions

I'm currently trying to implement a FEM to solve a type of wave equation with homogeneous Dirichlet boundary conditions by using standard $\mathcal{P}_1$ triangle elements and an explicit scheme for ...
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2answers
93 views

What would be a simple approach to validate a wave propagation code?

I have a linear elastic wave propagation code and an elastoplastic wave propagation code based on FEniCS. For now, I keep the 2D mesh (100, 100) fineness unit square and give a source wave of $\sin(...
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20 views

monitor functions for mesh generation: error estimate by FD or by FEM?

I am using a local truncation error estimate as the monitor function for adaptive mesh refinement that comes from a finite difference(FD) scheme and its values are available only at nodal points. ...
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1answer
38 views

imposing “measured data” to Dirichlet boundary conditions in fenics

I'm relatively new to fenics and I just looked through all questions related to Dirichlet boundary conditions. I don't seem to find a well-described question or answer about what I'm about to ask. I'...
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34 views

How to add a Ricker Wavelet (Mexican Hat) to a 2D/ 3D fem mesh?

I have a 2D square mesh and a 3D beam shaped mesh and I want to propagate a seismic wave in them. I am trying to simulate them using Open source FEM codes (fenics). I have left the top surface to be ...
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51 views

Reaction-diffusion equations

I'm simulating a biological phenomena with reaction diffusion equations. There are multiple diffusing materials and there are some complex relations about consumption and production of such materials. ...
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47 views

Weak form for elastoplastic wave propagation

I am trying to simulate elastoplastic seismic wave propagation using Fenics Solid Mechanics Application. The app. provides some quasi-static demos to show elastoplastic behaviour in a cube/ beam/ ...
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98 views

Effects of Lumping Mass Matrix

I've recently finished an introductory course on the finite element method from a more mathematical perspective (following Brenner and Scott) and we were introduced to the finite element mass matrix ...
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1answer
55 views

Can singularity screw up your model?

I've been running some complicated Finite Element Models. In most cases, the stress repartition seemed to be absolutely correct. However, on several point (complicated geometry), it appears that ...
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1answer
86 views

Space-time Galerkin of Burgers changes the convection speed

tldr: Can space-time Galerkin schemes applied to convection-diffusion problems lead to effects on the convection velocity? For time $t\in (0,1)$ and the spatial variable $\xi \in (0,1)$, I am ...
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1answer
70 views

How is the mass matrix formed in finite element methods? [closed]

as i am doing project on mass matrix, i want to know how to develop mass matrix. so please explain me how to develop mass matrix in detail.
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1answer
76 views

Finite element error for second order ODE at nodes equal to zero

I coded a finite element method with linear basis elements for the problem $$-u'' = f(x), x\in[0,1], u(0) = u(1) = 0$$ The nodes are uniformly spaced and I will denote them as $x_i$. I initially ...
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0answers
43 views

Pressure boundary condition in Navier-Stokes equations

I would like to solve 3D transient incompressible Navier-Stokes with FEM, Newton method, Schur-based preconditioner, Lagrangean P2/P1 elements (no stabilization), in a rigid pipe discretized with ...
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2answers
52 views

General Lagrange basis formula (usual problem in finite element context)

It is easy to prove that, $$\{p_1(x,y)=1-x-y\;,\;p_2(x,y)=x\;,\;p_3(x,y)=y\}$$ is a Lagrangian basis of $\mathbb{P}_1(\hat{T})$ (polynomials of total degree less that 1 living on $\hat T$), where $\...
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61 views

Efficient solution of large systems of non linear algebraic equations

I have quite simple problem of FEM solution of 1D differential non-linear equation. Altough the problem itself is simple, the numerical solution of the arising system of non-linear algebraic equations ...
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29 views

Problem with Levenberg-Marquardt for FEMU case

I m trying to implement a Levenberg-Marquart on python to identify 2 material parameters via Finite Elements calculations and full-field measurements as called FEMU (Finite Elements Model Updating). ...
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54 views

Does a mixed method solve this elliptic pde exactly if the source function is piecewise polynomial?

Let $\Omega\subset \mathbb{R}^d$, $d\in \{2,3\}$ be an open bounded polygonal/polyhedral set. Suppose I want to solve the following pde \begin{align*} \vec{q}+\vec{\nabla}u &=0\,&x&\in \...
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45 views

Solving system of constrained linear and non-linear equations in MATLAB

Solving system of constrained linear and non-linear equations in MATLAB I'm solving a FEM problem in MATLAB with use of the direct stiffness method. The problem is now formulated as a system of nn ...
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43 views

FEM asynchronous assembly

I would like to implement nonlinear preconditioner along with nonlinear additive schwarz. I wonder if there is any scientific FEM package, which allows for asynchronous assembly? (I need assembly ...
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1answer
39 views

NONLINEAR ENERGY MINIMIZATION EXAMPLE

I am learning about FEM methods and nonlinear optimization. I would like to try my nonlinear trust region solver on some simple nonlinear problem. What would be good example to implement for ...
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152 views

Once and for all: Which FEM plattform should I use for a very large multiphysics simulation?

I'm fooling around with the decision on how to build a multiphysics simulation for too long now (also several questions in this forum). First, I thought it would be possible/necessary to write most of ...
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1answer
59 views

FEM, Direct Stiffness Method with a nonlinear displacement constraint in one node

i have a question about a FE problem im working on. I made a finite element model of an linear elastic block of material (double striped block) attached with a rigid connection to the environment (...
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90 views

Role of the numerical flux in DG-FEM

I am learning the theory behind DG-FEM methods using the Hesthaven/Warburton book and I am a bit confused about the role of the 'numerical flux.' I apologize if this is a basic question, but I have ...
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47 views

What does a negative time stepping mean? (Adaptive time stepping)

Summary behind the problem: The following code aims at solving a static elasto-plastic problem. Like a 2D square mesh based on an elasto-plastic constitutive model like Von-Mises or Drucker-Prager ...
4
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1answer
81 views

Weak Formulation of Helmholtz equation with a complex coefficient and complex source term

I'm trying to solve $$\nabla^2u + ku = f\text{ in } \Omega,$$ $$u=0 \text{ on }\partial\Omega,$$ where $\Omega$ is a unit square and $k,f$ have real and imaginary components as $k=k_r+k_ij$ and $f(x,...
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1answer
45 views

FreeFem user-defined function [closed]

I'm trying to solve the steady-state heat equation with a space-dependent thermal diffusivity in FreeFem. I.e. $$\nabla\cdot(\kappa(x,y)\nabla T) = 0$$ I'm hoping to read in from a file locations $(...
3
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1answer
61 views

Projecting a vector field onto a H(div) space

I've got a uniform quadrangular mesh and for each node there's a vector quantity $u$ defined. I also have a non-aligned material interface across the mesh. Now I need that vector quantity to have a ...
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408 views

What is a common file/data format for a mesh (for FEM)?

I'm developing an FEM simulation. For early testing, I will use simple self-written mesher and visualisation of the mesh graph. But I want to prepare my program to use data generated by an existing ...
6
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2answers
72 views

Stokes Equation in “two-fold saddle point” form?

Are there papers that deal with the (nondimensionalized) Stokes equation for incompressible fluid flow in a "doubly mixed" form like the following? \begin{align*} 0&=\underline{\epsilon} + \frac{...
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25 views

Is it reasonable to use B-splines to compute a radial symmetric electrostatic field?

When I use normal finite elements to compute the electrostatic potential, then the electric field itself is discontinuous at the interfaces of two cells. This impacts how electrons can be tracked ...
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124 views

Nodal basis functions and lagrange polynomials

I am a bit confused with nodal basis functions $h_i$ and the corresponding lagrange polynomials $l_i$. For linear functions, it's quite clear, on $[x_0,x_1]$ the nodal basis is $h_0 = l_0 = 1-x$. But ...
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1answer
88 views

Derivation in the FEM method

Can any on help me understand how from the simple delta function on the right hand and performing the integration we can get values as in the left? Note that $h = x_i + 1 - x_i$ The diffusion and ...
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2answers
62 views

The second variation of displacement interpolation function in Finite Element Method

I need to calculate the second variation of displacement interpolation function $u = \sum N_a u_a$ in Finite Element Analysis, where $N_a$ are the shape functions and $u_a$ are the nodal values. ...
4
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1answer
43 views

In mixed elliptic formulation, what are the weakest requirements to ensure the flux is in $H^1$?

In the book Mixed Finite Element Methods and Applications by Boffi, Brezzi, and Fortin there is a pretty long discussion about why the Raviart-Thomas (RT) projection is only defined for functions in $...
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1answer
68 views

Discretization of lifting operator in BR2 scheme

The lifting operator $\mathbf{r}(\mathbf{v_h})$ for the '2nd version' of Bassi-Rebay scheme for elliptic problems in $d$ dimensions is defined as $$ \int_{\Omega_h} \mathbf{w}_h \cdot \mathbf{r}(\...
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1answer
63 views

weak form of an equation by continuous discontinuous galerkin method

If we have the weak form of an equation like Poisson equation with discontinuous Galerkin method, to get the weak form of continuous discontinuous Galerkin method what terms are changed? Is it true ...
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80 views

Galerkin FEM error when using even number of elements

Intro: I am developing a Galerkin FEM code in matlab - starting small with a simple 1D ODE. The equation I'm trying to solve is: $$a u_x = cos(x), x \in [0, 2\pi]$$ Which has a known exact solution $$...
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24 views

Estimate in Minimal Dissipation Local Discontinuous Galerkin Method

I am going through the paper titled "An analysis of the Minimal Dissipation Local Discontinuous Galerkin Method for Convection-Diffusion Problems", written by Cockburn and Dong. In section 3.1 of ...