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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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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71 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
40 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
56 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
65 views

How is the mass matrix formed in finite element methods?

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
67 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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38 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
49 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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1answer
60 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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27 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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1answer
53 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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39 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
38 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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38 views

I'm comparing two different methods for solving the Navier Stokes equations. Why are my velocity results so different?

I just posted a question with this exact title at the "Mathematics" part of Stack Exchange and someone directed me here. Apologies if it is not OK to double-post. I want to use a code for modeling ...
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149 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
54 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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86 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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45 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 ...
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1answer
79 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
44 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 $(...
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1answer
59 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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4answers
383 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 ...
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2answers
70 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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3answers
120 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
85 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
61 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. ...
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1answer
41 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
66 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
62 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 ...
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65 views

Solving a nonlinear poisson equation via variational minimization

I am kind of new in finite elements and I am solving simple "Poisson nonlinear" problem. $- \nabla ((1 + u^2) \nabla u) = f$ $u = 0 \ \text{on} \ \Omega $ I am using Newton solver, where I have ...
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1answer
46 views

How to find $L^2$ error for discontinuous Galerkin method

In standard finite element method, when we want to find $L^2$ error of a solution, we only find the error on Gaussian points that are inside of each triangle, for $DG$ method can we do this in a same ...
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1answer
70 views

How to construct shape functions in the $L^2(\Omega)$

It is necessary for me to find the shape functions on $L^2(\Omega)$(piecewise constant functions), I searched a lot but that, could not find anything, all of them are about higher degree polynomial. ...
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1answer
246 views

Intro to DG Finite Element methods

I wrote a number of 1D/2D FE and FD programs as a bachelor student, but the main problem I continually came into contact with was gradient shocks related to convection/diffusion problems in convection-...
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46 views

Check the well-posedness of the problem with level set equation

Given a domain $\Omega$ with 2 subdomains $\Omega_1,\Omega_2$ as figure below Level set equation $$ \partial_t\varphi + U\cdot\nabla\varphi =0 $$ $U$ is velocity only presents inside $\Omega_1$. ...
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71 views

CFD implementation in software [closed]

I've been learning CFD theory for 4 months (which includes FEA, FDM AND FVM) and now I want to start running simulations. As a novice to CFD software, I would appreciate some advice on where to start, ...
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137 views

how to solve a 2D non-linear Poisson equation?

I am trying to solve the following equation for $P(x,y)$: $$I = P \nabla \cdot \frac{1}{P^2} \nabla{P}$$ where $P$ and $I$ are functions of x and y. $I(x,y)$ and $P(x,y)$ I want to understand ...
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63 views

Is there a difference between the Galerkin MWR and other techniques called Finite Element Method [closed]

Recently, I took a course on numerical methods where we learned about Galerkin's Method of Weighted Residuals. We were told that it forms the basis of the Finite Element Method . However, in most ...
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1answer
40 views

Different Meshes Different Maximum velocities

I am working on a model in COMSOL and I am usin different meshes from coarse to fine keeping the other parameters constant. And, I got different maximum velocities for all the meshes. What can I do ...
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35 views

Representing a 3D system in 2D (Electromagnetic modelling)

Ok so I'm a complete beginner in computational modelling (I use analytical methods of physics typically) but I would like to model an anisotropic, aperiodic (but not random) finite array of metallic ...
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56 views

How to build semiconductor 1-D p-n diode model in COMSOL?

I don't have access to the semiconductors' module, thus I am building my own P-N model. I assumed there would be 4 intervals, ...
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1answer
74 views

How to create node to node lumping

I have been doing finite element analysis using Matlab. I look for many examples and tutorials producing only the stiffness matrix letting elements being weightless. However, in my case i need to do a ...
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1answer
180 views

What are differences between 'a priori' and 'posteriori' error estimate in numerical analysis?

I have learnt about Finite Element Method (also a little on other numerical methods) but I don't know what are exactly definition of these two errors and differences between them?
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102 views

Jump conditions on interior boundaries

I can not undrestand when we have jump on interior boundaries, if the solution be continuous. In the interior boundaries, derivatives have only different unit outward normal vector and this means we ...
4
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1answer
138 views

Simulate electric fields due to surface charges in simple circuits using python

I want to simulate the electric fields in simple circuits using Python and only free software. My first goal is to reproduce the images given in (1) which are made by the commercial ANSYS Maxwell ...
3
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3answers
105 views

How to assemble Global matrix (for coupled) problem?

I'm trying to assemble global matrices for the following system. $$ \begin{bmatrix} K& Q\\ Q^T&S \end{bmatrix} \begin{bmatrix} u_h\\ p_h \end{bmatrix} = \begin{bmatrix} f_u\\ f_p \end{...
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1answer
78 views

Finite element method applied to variational problem/functional VS weak formulation

I am confused. I read an introduction to finite element method where it was derived for the poisson equation: $$-\Delta u + cu = f,\qquad, u = g_0 \text{ on Dirichlet boundaries},\qquad\partial_n u ...