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 ...

learn more… | top users | synonyms (1)

0
votes
1answer
23 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 ...
0
votes
0answers
28 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 ...
0
votes
0answers
17 views

Normal Velocity Gradient to wall in turbulent flows [on hold]

I working on simulation of Low-Reynolds Turbulent flows (Chein's Model). I am stuck in a middle and probably something with a simple solution, In order to calculate the term $ \begin{align} y^+ ...
3
votes
0answers
121 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 ...
0
votes
1answer
39 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 ...
0
votes
0answers
20 views

PML setting goes wrong in COMSOL multiphysics [closed]

I am working on a nano-optics case using COMSOL multiphysics 4.2a, My model includes a (450nm)(450nm)(450nm) computation domain Unit amplitude EM Plane wave: $e^{-2\pi i n y/\lambda}$ is sent into ...
4
votes
0answers
70 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 ...
0
votes
0answers
42 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
votes
1answer
75 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 ...
1
vote
1answer
42 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
votes
1answer
57 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 ...
9
votes
4answers
366 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
votes
2answers
68 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} + ...
0
votes
0answers
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 ...
1
vote
3answers
118 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 ...
0
votes
1answer
79 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 ...
1
vote
2answers
59 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
votes
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 ...
1
vote
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 ...
0
votes
1answer
60 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 ...
5
votes
0answers
78 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 ...
0
votes
0answers
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 ...
2
votes
0answers
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 ...
0
votes
1answer
44 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 ...
1
vote
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. ...
4
votes
1answer
242 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 ...
0
votes
0answers
45 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 $\Omega_1$. ...
1
vote
0answers
69 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, ...
0
votes
0answers
134 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 ...
1
vote
0answers
61 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 ...
0
votes
1answer
39 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 ...
1
vote
0answers
34 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 ...
0
votes
0answers
49 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, ...
0
votes
1answer
70 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 ...
11
votes
1answer
160 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?
1
vote
0answers
101 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
votes
1answer
105 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
votes
3answers
102 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 ...
1
vote
1answer
75 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 ...
2
votes
2answers
174 views

FEM libraries with weak forms

I need to implement a structural analysis code, and I turn to you for advice. My needs are simple: Library must be integrable in a C++ code I want to express a weak form, without manual intervention ...
3
votes
1answer
107 views

Convergence of the second derivative of the finite element solution

Let $u_h$ be the finite element solution of a fourth order equation (like biharmonic equation), using polynomial degree two. If the convergence rate of $u_h$ is $2$, what is the convergence rate of ...
4
votes
2answers
134 views

FEM: Obtaining the Weak Form

In the the Finite Element Method (FEM), we attempt to obtain the Weak Form of the described equation. I understand that this is an attempt to reduce the order regularity of the equation, but what are ...
2
votes
3answers
84 views

Angle of rotation at a point in a deformed triangle

I have a 2D triangle which deforms with each vertex moving by some small ($\sin(x) \approx \tan(x) \approx x$) displacement vector. The displacement of any point in the triangle is linearly ...
1
vote
0answers
59 views

Solving system of equations with zeros on diagonal [closed]

I am using finite elements, Newton Raphson technique and MUMPS direct solver, to solve for $P$ in this equation: $$\frac{\delta K}{\delta x} \frac{\delta P}{\delta x}= \frac{\delta K B}{\delta x} + ...
3
votes
1answer
76 views

Continuous vs discontinuous pressure elements in fluid flow problems

When solving fluid flow problems using finite elements you typically end up requiring that $p\in L^2$. For Darcy flow problems, a popular choice of elements is the Raviart-Thomas element and ...
6
votes
1answer
54 views

Approximation properties of FEM projections operators on a boundary

We have an elliptic projection $$P: V \rightarrow V_{h}$$ which satisfies $$\Vert u - Pu \Vert_{L^{2}(\Omega_{e})} \leq Ch^{k+1} \enspace .$$ Can we say anything about $\Vert u - Pu \Vert_{L^{2}( ...
0
votes
1answer
66 views

How to deal with transition elements in adaptive fem

It is necessary for me to solve a Poisson equation by adaptive finite element method with transition elements technique to get conforming mesh. For the first local refinement everything is OK, ...
8
votes
5answers
500 views

Choice of basis in FEM

Briefly, what are the different types of basis used in FEM and why is the nodal basis so popular and advantageous in the finite element context?
2
votes
2answers
120 views

Finite element results by different meshes

There are some technique to generate mesh in a domain. My qustion is that: Is there any difference between the results using different techniques for mesh generation? If yes which one is better. For ...
3
votes
1answer
83 views

Gradients on 2D FEM Triangular Mesh

A scalar field f approximated on a triangular mesh using the FEM method can be given as $f(x,y) \approx \bar{f}(x,y) = \sum_{n=1}^3 \left(\phi_n(x,y) \cdot f_n \right)$ I am of the understanding, ...