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
2answers
38 views

Is “tangent stiffness matrix” the same as “stiffness matrix”?

I'm trying to implement nonzero Displacement Boundary Conditions in VegaFEM on a non-linear model, using the method outlined in §3.6.2 of University of Colorado's intro to FEM (modify $f = Ku$: set ...
2
votes
1answer
49 views

The meaning of conservative discretization in Galerkin FEM and Discontinuous Galerkin

I do understand the meanning of "conservative discretization" within the FVM/FDM framework, indeed it is well explained in this post. Now, according to the table in this slide (pp.4), it concludes: ...
0
votes
1answer
50 views

Finite element method for odd order DE

What are theoretical hurdles in applying Galerikin method on, say, first order time dependent ODE? Is there no way we can form an inner product??
2
votes
1answer
26 views

Shell vs frame element model stiffness differences

I have a model of a tall, slender structure that I am investigating using both shell and 3D frame elements. The shell elements are type MITC4, 4-node membrane elements. The frame elements are the ...
2
votes
1answer
63 views

Inverse isoparametric mappings for quadrilateral finite elements

I have an isoparametric mapping $F_{E}: \hat{E} \to E$ where $\hat{E}$ is a reference quadrilateral (square) and $E$ is some quadrilateral in the domain $\Omega$. If $E$ is a parallelogram, then the ...
3
votes
1answer
117 views

Boundary conditions in conforming Galerkin method for biharmonic equation

I am trying to solve simple scalar biharmonic equation using bubnov-galerkin finite element method. I am using $H^2$ conforming basis functions. I was wondering that if anyone can give me some ...
4
votes
1answer
84 views

Find the direction of the gradient on a finite element mesh

Suppose we have a triangular mesh of a two dimensional shape $\Omega$, and on this mesh we define a P1 finite element structure. I know that given $u,v$ by their values at the vertices of the ...
0
votes
0answers
40 views

Best way to average surface data or function data in 2d grid

I have pressure data on a 2D triangular surface. I can compute average(data). What is the best way to average the surface data?
0
votes
0answers
12 views

What is the elastic constants for tetragonal zirconia (GPa)? [migrated]

I have known six constants of TZP, what is the relationship between the known and the unknown? known: c11 = 327, c12 = 100, c13 = 62, c33 =264, c44 = 59, and c66 = 64 (units: GPa) unknown: all the ...
4
votes
1answer
36 views

Estimating the local compression/expansion ratio for a transformation on a point cloud

Let's say we have an unorganized point cloud P1 with N points, each with coordinates {x,y,z}. We apply non-rigid transformation to P1 (translation + rotation + warping), to obtain point cloud P2. ...
0
votes
1answer
56 views

FEM - Shape function of a HEX20 - plot in MATLAB

I have a FE model of a simple plate with hole (tension load) with HEX20 mesh. I need to obtain the Shape Function of one of the elements (the one with highest stress) and plot it (with MATLAB). After ...
0
votes
0answers
60 views

Conditions for always positive gradient of heat field in evolutionary thermo-elastic system

I am investigating stability and convergence of series of approximations for coupled thermoelasticity problem yielded by one-step recurrent time-integration scheme. I've managed to show that the ...
0
votes
2answers
59 views

Finite element programming tutorial [closed]

I am new to this site and it might therefore not be the best place for this question. I have been using finite element programs (CFD mainly) for some time and I want to learn more about the basics. ...
6
votes
1answer
133 views

How to project a vector into the H(div) space (in the context of finite elements)?

Say I have a simple elliptic PDE: $$ -\nabla\cdot(K\nabla p) = f \;\;\;\text{in}\;\Omega $$ with the appropriate boundary conditions. I solve for $p$ using a FEM (a discontinuous Galerkin method to ...
6
votes
1answer
62 views

Space-time finite element discretization for time-dependent PDEs

In FEM literature, semi-variational methods are typically used in the solution of time-dependent PDEs. I have not seen a fully-variational approach i.e. where space and time are discretised by FEM, ...
1
vote
0answers
49 views

Determining Youngs Modulus of defined material in FEA (ABAQUS)

I am quite new to FEA but need to determine if I am performing my simulations correctly. I have a cube of material with defined elastic properties (Youngs Modulus and poison ratio). I perform a ...
6
votes
1answer
95 views

How to avoid negative values of numerical solution of transport equation using FEM scheme?

The transport equation is actually an advection-diffussion-reaction equation, which has the form as $$\frac{\partial C}{\partial t} + v_1 \frac{\partial C}{\partial x} + v_2 \frac{\partial ...
1
vote
1answer
49 views

Reaction-Diffusion problem A->B, solving for B

I need to solve a Reaction-Diffusion using Finite Elements, piecewise linear elements. In this problem, a reaction $A \rightarrow B$, with rate law $ r_A = - k_A \cdot u_A $, takes part, where $u_i$ ...
1
vote
0answers
41 views

Can variational formulations be solved using series solutions?

What I specifically mean is, given some functional $F\left[\mathbf{x}\right]$ which is stationary with respect to $\dot{\mathbf{x}}=f(\mathbf{x})$ and some boundary or initial conditions, can one ...
3
votes
1answer
57 views

Solving pure Neumann problem enforcing B.C. with Lagrange Multiplier

I want to solve the Laplace Equation with pure Neumann B.C. using Finite Element Method: $- \Delta u = f \ $ in $ \ \Omega $ $- \partial u/\partial n = g \ $ on $ \ \Gamma = \partial \Omega$ With ...
2
votes
1answer
74 views

Best preconditioner for mixed-poisson problem (RT0 elements)

For a very large mixed-poisson problem with lowest order Raviart-Thomas elements (RT0), I plan on using an iterative solver. However, this kind of problem is not positive-definite (saddle point ...
5
votes
2answers
141 views

How do hexahedral FEM meshes improve approximation quality per degree of freedom, compared to tetrahredal meshes?

From the deal.II FAQ : ...quadrilaterals and hexahedra typically provide a significantly better approximation quality than triangular meshes with the same number of degrees of freedom; you ...
1
vote
1answer
139 views

Step-wise finite element formulations: can this be done?

Given the functional: $$ F[\mathbf{x}]=\frac{1}{2}[\mathbf{x}^{\text{T}} * D(\mathbf{x})]-\frac{1}{2}[\mathbf{x}^{\text{T}} * \mathbf{Ax}]-\frac{1}{2}\mathbf{x}^{\text{T}}(0)\mathbf{x}(t) $$ Where ...
9
votes
3answers
157 views

Finite elements on manifold

I'd like to solve some PDEs on manifolds, say for example an elliptic equation on a sphere. Where do I start? I'd like to find something that use preexisting code/libraries in 2d , nothing so fancy ...
4
votes
1answer
163 views

Why are functional representations of systems important in numerical applications?

I tried asking a similar question in SE.Physics, and I got some information regarding the abstract side of this, but I figured I should post here to get more complete information about the numerical ...
3
votes
0answers
50 views

Creating FEM mesh for image region — what is the most suitable shape function?

I wish to create a FEM mesh to solve an inverse elasticity problem, for an irregular domain. This domain is given by a medical image, so it is discretised and each square on the grid has one scalar ...
0
votes
0answers
28 views

Resources for viscous behavior in simple FEM

I am working on a simple explicit-integration lumped-mass elastic FEM code which implements CST+DKT triangles (plate+shell) and constant-strain tetrahedra ...
3
votes
2answers
100 views

Why do structured and unstructured discretizations give different errors?

It is necessary for me to solve a Poisson problem with a numerical method on a square domain with two types of triangular mesh: uniform triangular mesh (using uniform distribution nodes on square) and ...
9
votes
2answers
102 views

Finite elements $W^{1,\infty}$ error estimates

Are there finite element method setups that provide error estimates in the $W^{1,\infty}$ norm (i.e., bounds on $\|u'_h - u'\|_\infty$)? Which families of elements can be used for implementing them? ...
0
votes
1answer
54 views

Solving Initial Value problem ignoring the time-derivative

I am looking at a heat initial value problem \begin{align} \frac{\partial u}{\partial t}-\nabla^2u = f\quad&\text{in}\quad \Omega\times(0,T)\\ u = g \quad&\text{on}\quad ...
3
votes
2answers
138 views

Initial Value Problem using Finite Element

I am trying to implement a FEM solver for the following initial value problem \begin{align} \frac{\partial u}{\partial t} - \nabla^2 u &= f\quad \text{ in } \Omega\times (0,T)\\ u &= g\quad ...
1
vote
0answers
63 views

Thin plate stiffness: analytical formula to validate FEM model

I tried to compute analitically the stiffness of a cantilever thin plate (shown in picture). The plate is also homogeneous and isotropic. The aim is to compare the result I obtain with the result I ...
0
votes
1answer
141 views

How to solve Energy Balance equation by numerical method

Good Day I am new to heat transfer technique please give me some suggestion on solving energy balance equation $$a \frac{\partial T_p}{\partial t}=\frac{\partial}{\partial x}\left(b\frac{\partial ...
2
votes
2answers
96 views

Model of heat sink problem with fan

I am trying to solve this problem using advection-diffusion model and finite element method for the solution, due to the complex geometry. Basically the problem i'm trying to solve using OpenFOAM is ...
5
votes
1answer
102 views

Effect of subdomain topologies on overlapping additive Schwarz?

Is there a reference on the effect of subdomain topology on performance of the overlapping additive Schwarz method for (high order) finite elements? For example, taking subdomains to be vertex ...
3
votes
2answers
178 views

Projecting Finite Element solution onto new mesh

I am implementing a finite element solver in MATLAB and I have the following problem. Let's say I have a mesh $\mathcal{T}_1$ with triangular elements on a rectangular domain ...
0
votes
1answer
89 views

Importing results of FEM analysis into Matlab

I need to import in Matlab the results (like time histories of diplacement or frequency response at a specific point) obtained from a FEM analysis in Nastran. At the moment I ask Nastran to save the ...
4
votes
2answers
224 views

P versus Q elements

I am currently developing a project that uses finite elements for multi-dimensional PDEs and I'm still wondering if I will use P elements (triangles in 2D and tetra in 3D) or Q elements (squares in 2D ...
0
votes
2answers
80 views

Structural FEM analysis: transiet response vs frequency response

I am running 2 simulations on a cantilever plate in Nastran: one is a transient analysis (time domain) and the other one is a frequency response analysis. The transient analysis computes the response ...
3
votes
0answers
141 views
+50

Is it possible to predict the null space of a structure from contributing elements null spaces?

I am trying to solve an almost incompressible problem with heterogeneous properties by domain decomposition. Solution with CG converges slowly or divergerces completely. My problem becomes ...
2
votes
2answers
187 views

Why does FEM usually formulate the problems in reference configuration?

I'm with the background of computer engineering and generally use FEM for graphics simulation. As far as I know, FEM formulation is usually expressed with respect to the reference configuration, i.e., ...
1
vote
2answers
76 views

How to determine the support/influence domain for irregularly distributed nodes in the Element-Free Galekin Method?

EDIT (26-12-14):In the Belytschko's EFG code, the domain of influence for uniform distributed node can be calculated using the code below; my question is how to calculate xspac and yspac when the ...
0
votes
1answer
302 views

Alternatives to Comsol Multiphysics

This might be a question better suited for the Software Recommendations side of S.E., however I do believe that people who frequent this part of S.E. are more likely to be able to answer this ...
2
votes
2answers
164 views

FEM for a nonlinear parabolic PDE

I'm looking to numerically compute the solution to $$ k(x,u) \partial_t u - \Delta u = f \quad\quad\text{ in } \Omega \times [0,T]$$ where $k$ is a continuous but nonlinear (in $u$) real-valued ...
0
votes
1answer
85 views

What is Mesh Independence Report?

I am performing analysis on chassis (Static Structural) and for optimization purpose i am asked to generate MESH-INDEPENDENCE REPORT,of which i have no idea. I have tried going through research papers ...
1
vote
1answer
116 views

Solve steady state reaction-diffusion/Helmholtz equation numerically

I am solving a problem of the form: $\dfrac{\partial u(x,y,t)}{\partial t} = \nabla^2 u(x,y,t) - f(x,y,t)u(x,y,t) - \kappa(x,y,t)$ At the moment, I am solving this at each time step by assuming a ...
1
vote
3answers
131 views

Solve diffusion equation with linear source term

I would like to solve numerically the diffusion equation, where the sink term depends linearly on the field, and there is field-independent sink: $\frac{\partial^2 u(x)}{\partial x^2} =f(x)u(x) - ...
4
votes
4answers
210 views

Motivation behind Galerkin method

I have a question about Galerkin method. I don't understand why the Galerkin method weights the residual by the shape functions and sets it equal to zero. I want to know what is reason of this. Why we ...
2
votes
1answer
247 views

Finite Element integration with tensor notation

While I was studying discontinuous finite element methods I found an integration of a Navier Stokes equation using tensorial notation. The equation is the following: $\mathbf{\bar {u}}_{t} + ...
4
votes
4answers
264 views

Need a simple mesh format (for FEA) and a tool to generate the mesh

I want to write a 2D FEA code for my course project and I need to import a mesh (2d, simple quad/tri) on a simple geometry such as a L shaped plate or with a square/circular hole in it, something like ...