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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26 views

High frequency noise at solving diffusion equation

I'm trying to simulate a simple diffusion based on Fick's 2nd law. ...
2
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0answers
40 views

Beam finite element stiffness matrix from section constitutive matrix

I'm trying to construct the 12 x 12 beam element stiffness matrix from a section constitutive matrix (6 x 6 with shear stiffnesses, axial stiffness, bending stiffnesses and torsional stiffness on the ...
3
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1answer
103 views

Recommendations on FEM software for implementing Nitsche's method on interfaces between matching meshes?

Suppose: I have two domains, $\Omega_{1} = [0, 1/2] \times [0, 1]$ and $\Omega_{2} = [1/2, 1] \times [0, 1]$. The domains share an interface $\Gamma = \{1/2\} \times [0, 1] = \partial\Omega_{1} \cap ...
2
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1answer
135 views

Good Finite Element Library for a small project

I'm currently working on this project and I have a basic structural analyzer that uses the finite element method. Essentially, I turn each block into a set of trusses, construct a stiffness matrix ...
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0answers
71 views

Derivation of the weak form and discretization of a Helmholtz equation for FEM

I need help solving the following problem: The strong form of the three-dimensional modified Helmholtz’s equation reads: $$ e-c\nabla^2e=b $$ where $e$ is a scalar field ($e=e(x)$) and $b$ and $c$ ...
6
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1answer
77 views

L1 functional setting for Navier-Stokes with finite elements

Typical finite element problems assume $L^2$ which is a Hilbert space, but I've heard that $L^1$ for Navier-Stokes results in less overshoots/undershoots, but $L^1$ is not Hilbert. The dual space for ...
4
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1answer
124 views

Which finite-element framework allows the easy implementation of HDG methods?

I have tinkered around with the implementation of hybridizable Discontinuous Galerkin (HDG) methods in DUNE-PDELab and DUNE-FEM for my PhD but since then I have not had the time to work on these codes ...
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2answers
89 views

How to find the smallest positive eigenvalue of a large general system if they are all in +/- pairs of real eigenvalues

I used MKL Lapack SBGVX because it can solve for "selected" eigenvalues/modes (both positive and negative), thinking it would be efficient, but it is extremely slow when compared with Bathe's subspace ...
3
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1answer
115 views

Crouzeix-Raviart Finite Element

Can anybody recommend me a good introduction to Crouzeix-Raviart Finite Elements? Their motivation is not obvious and the body of literature is hard to overlook.
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5answers
182 views

Is discontinuous Galerkin really any more parallelizable than continuous Galerkin?

I've always heard that easy parallelization was one of the advantages of DG methods, but I don't really see why any of those reasons don't also apply to continuous Galerkin.
2
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0answers
35 views

Modal analysis of structure with aerodynamic damping

I'm using modal decomposition to predict the steady state response of a beam structure to harmonic loading. The structure itself is very lightly damped, but we know from experiments that the ...
0
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1answer
57 views

How does Abaqus calculate Hill's function for non-rectangular coordinate systems?

Within the manual, the effective/von Mises stress or Hill's potential for anisotropic bodies is calculated in Abaqus in cartesian rectangular coordinates as $\sigma_{eff}=\sqrt{I_{1}^{2}-3I_{2}} \\ ...
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2answers
197 views

Which novel data structures are used in adaptive FEM?

A lot of adaptive FEM libraries use more advanced mesh data structures to handle adding/removing nodes, edges, triangles, tetrahedra, etc. For example, the p4est library uses octree data structures ...
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0answers
53 views

The shape function of the corner point from a serendity element (Q8)

For a serendipity element, the shape function of a middle pt on a edge can be formed using the tensor product in each direction e.g. pt 5 on Quad8 $$ \phi_5(\xi,\eta)=\frac{1}{2}(1-\xi^2)(1-\eta) $$ ...
2
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2answers
104 views

In what regime do the continuous and discontinuous Galerkin method become unstable for advection-diffusion systems?

I know that the finite volume method (based around a central different stencil) is unstable for advection dominated advection-diffusion problems. This leads to different adaptive schemes to can be ...
1
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0answers
52 views

Locally conservative method for differential generalized eigenvalue problem

I have to approximate the smallest eigenvalue of the following generalized eigenvalue problem $$ - \nabla \cdot D(x) \nabla p(x) + \alpha(x) p(x) = \lambda \beta(x) p(x) $$ over a domain like ...
2
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1answer
67 views

Extended finite element method vs $P_k$-bubble element

Can you show me the main differences between 2 methods? I find out 2 reasons but I don't know they are right or not. XFEM is constructed base on enrichment functions whereas P1-bubble is constructed ...
7
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2answers
139 views

The effect of decoupling a coupled system of PDEs

I asked a somewhat similar question previously but perhaps it might have been too specific for anyone to really answer. Here is a bit more general of a question that I am struggling with. Consider the ...
8
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3answers
441 views

Finite Element Method vs Extended Finite Element Method (FEM vs XFEM)

What are main differences between FEM and XFEM? When should we (not) use XFEM intead of FEM and vice versa? In other words, when I meet a new problem, how I can know to use which one of them?
3
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2answers
159 views

Consumer GPUs for sparse matrices (e.g. FEA)

Are consumer grade GPUs (like the NVidia Geforce series) used for solving sparse linear equations systems in a professional setting? For example, by engineers performing finite element analysis? ...
5
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0answers
93 views

Sequential approach to solving coupled PDEs

I'm dealing with a coupled system of three transient, non-linear convection-diffusion equations. Let's just say to simplify the problem that they take the following form: $$ ...
4
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4answers
313 views

Basic explanation of shape function

well this is my first time posting here. I just started studying FEM in a more structured basis compared to what I used to do during my undergraduate courses. I'm doing this because, despite the fact ...
2
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2answers
105 views

What is the meaning of distortion in region outside of stressed geometry using FEA?

In FEA simulation of simple beams (3D solid and shell/plate), I have taken a simple geometry: A long beam in the y direction a concentrated load applied on the plane of symmetry There is a pin or ...
5
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0answers
76 views

Conjugate residual/gradient convergence checking in practice

Let's say we want to solve $Ax=b$ ($A$ symmetric positive /semi/definite) with the conjugate residual/gradient method. $A$ comes from FEM where the mesh is being refined. The exact solution is $x_*$ ...
5
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2answers
137 views

FEM+DDM applied to scalar Helmholtz - necessity of lagrange multipliers?

I am seeking to understand DDM's and their application to Maxwell's equations, though I am settling for the scalar Helmholtz as a baby step. Unfortunately I have hit a conceptual snag that I could use ...
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0answers
59 views

“Tie Constraint” in fenics solid mechanics

I am migrating from ABAQUS (primarily because the university decided to not buy the licenses any more). I am more of an analyst than a developer so please bear with me. I was working on a model that ...
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1answer
55 views

A 2D static problem with known analytical solution

I am looking for a 2D static problem (i.e. planar stress/strain) with known analytical solution. The purpose for that is to verify my self-written code in matlab for solving 2D static problems. Any ...
2
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1answer
154 views

How to derive the functional for a given differential equation using the variational expression?

In the attached image, I want to understand how to arrive at the equation 2.5.1, i.e. the variational expression. The problem is defined as best as it could and the further derivation follows ...
4
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1answer
103 views

Localization of Sub-problems in the Multiscale Finite Element Method

Background: I'm trying to understand the Multiscale Finite Element Method and I'm reading Effendiev & Hou (2009) Multiscale Finite Element Method. Suppose I'm working with a poisson equation of ...
2
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1answer
156 views

Implementation of gradient zero boundary conditon in advection-diffusion equation

My question is about Finite Element Method. I want to know how to implement "gradient zero" conditions to advection-diffusion equations in conservative form like, $\frac{\partial \rho}{\partial t} + ...
3
votes
2answers
101 views

Integrating an Ordinary Differential Equation over a domain in Finite Element Methods

I'm trying to get a deeper understanding of the Finite Element Method (FEM) to better understand what I do in COMSOL and FEniCS. The sketch below shows the problem that I want to solve in FEM. The ...
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0answers
41 views

how to find outward normal for robin codition [duplicate]

I wrote the code to fix this problem; now I should validate it using a test function to see the error in my code. I can't figure out how starting from u can derive the function g on the edge, in ...
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1answer
124 views

Pde problem with robin boundary condition

I have my pde 2D problem with robin condition (form: du/dn +ku=g) to solve with matlab. i have the exact function u and I want to find the function g in robin condition. How can i do it? thanks for ...
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0answers
31 views

library for Refine a tetrahedral volume domain over the intersection points of the edges and a level surface

I tried with fenics and tetgen but these libraries has not this functionality. an example is fenics fenics qa the idea is simple given a tetrahedrical domain $\Omega$ and a surface $\psi(x,y,z)=0$ ...
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0answers
53 views

Characteristic length of differential element of cylinder surface?

I am trying to find the Nusselt number for a small element of the outside of a cylinder that has a height of $\Delta z$. I found the average Grashof number of a surface as $$Gr_{L}=\frac{\beta \rho ...
3
votes
1answer
120 views

The Lax-Milgram Lemma in FEM with non-homogenous Dirichlet BC

How can show that the prerequisites for the Lax-Milgram Lemma holds if I have different test and trial spaces (which I think is the natural thing to have if at least part of the boundary is ...
6
votes
3answers
427 views

Visualizing finite element solutions in MATLAB

On my triangular mesh, I have the $(x,y,z)$ coordinates of each vertex of each triangle. For higher order elements, I refine each element a few times so I have more points to work with. If I just need ...
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0answers
74 views

Calculating Divergence in COMSOL

Is it computationally safe and accurate to use the following equation in COMSOL to compute the divergence of the vector quantity J (instead of using its general built-in equations that have $\nabla$ ...
3
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0answers
136 views

assembly matrices in finite element method

I'm trying to construct the right–hand side of my 2D Poisson's equation in Matlab. I used the vertex rule in order to approximate the integral: ...
3
votes
2answers
161 views

Slow convergence of Newton's method for finite elements

The application is a simple non-linear advection diffusion problem (steady state) using DGFEM. My error at each iteration is given by $$ e_{n+1} = ...
4
votes
1answer
112 views

Backward Euler time step for finite elements

For the backward Euler discretization in time: $$ \left( \frac{u^{(k)}-u^{(k-1)}}{\Delta t}, v\right) + a(u^{(k)},v) = \ell(v) $$ where $a(\cdot,\cdot)$ is the bilinear operator associated with the ...
5
votes
2answers
177 views

Finite element discretization of Reaction-diffusion problem with Dirac source term

I'm writing a code using continuous piecewise linear finite elements on triangular grids to solve the diffusion-reaction problem. the source function f is a Dirac mass at the center. How can i compute ...
3
votes
1answer
143 views

Convergence of interior penalty DG methods

I’m currently having some issues with my routine for the linear advection-diffusion problem. The model problem is as follows: $$ \nabla\cdot(\mathbf{s} u) - \nabla\cdot(\kappa\nabla u) = f, ...
4
votes
1answer
103 views

Is is possible to mix finite-volume and finite-difference discretisations when solving a coupled non-linear system?

In my last question I noticed a peculiar error when solving the Poisson equation using finite volume method (FVM), Peculiar error when solving the Poisson equation on a non-uniform mesh (1D only) ...
2
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0answers
174 views

Could you give examples of serious usage of meshfree methods?

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

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

I'm reading up on the Finite Element Method (in 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 ...
1
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1answer
99 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 ...
0
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0answers
197 views

Magnetostatic and magnetodynamic problems in freefem++

I would have liked to use freefem++ for implementing some simulations as in the title but I didn't find anything about it. I know it does implement Nedelec elements but I don't know for example how to ...
2
votes
0answers
84 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 $f(t_i, \cdot)$ ...
1
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3answers
247 views

Capacitance in freefem++

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