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# Questions tagged [finite-element]

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 estimates.

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### Continuous Finite Element vs Space Frames

Finite Element allows one to divide a continuous medium into a mesh and compute structural properties of it. Instead of discretizing the continuous, why not start with a discrete method to begin with? ...
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### How to generate mesh for space-time FEM method in FEniCS?

suppose that I have a region called $\Omega$,suppose that this is a 2D or 3D region, how to generate the corresponding space-time mesh by using FEniCS? and how to extract the boundary and implement ...
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### Rolling friction settings in COMMERCIAL (Ansys) finite element software

Is there a standard way of implementing rolling friction in COMMERCIAL finite element software? There's no book about such a subject in COMMERCIAL FEM software though there are books on algorithms ...
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### Quintic Hermite shape functions

I am trying to use quintic Hermite basis functions for FEM applications, could someone please direct me to the general formula that would help me generate quintic Hermite shape functions? In natural ...
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### FEA with order reduced for a large system with a very localized force application

I have a large structure with many DOFs. But the application of force is very localized say over one or two nodes. If I try to run FEA on this with Guyan Reduction, I think the efficiency of reduction ...
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### uniform refinement is not working in gmsh

I get 0 node and elements when I use -refine command line flag in gmsh. Explicitly writing RefineMesh; in the script produces the original mesh and not a refined one. Am I missing something while ...
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### Recommendations for some new books about computational contact mechanics in solid mechanics

I want to simulate some frictional contact problems, but I'm not familiar with this field, could you please recommend some new books as introductions?thank you
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### 3D Quadrature schemes with points on boundary

In one dimension there are two types of quadrature schemes. asymmetric rules like Newton-Cotes like formulas (Trapezodi, Simpson), and Clenshaw-Curtis place sampling points on boundary of the ...
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### How to determine whether the symmetric stiffness matrix is positive definite or not? Is it related to the problem?

For two-dimensional or three-dimensional elliptic equations, when will the stiffness matrix be asymmetric and positive definite? This affected the solution efficiency so much that I had to choose an ...
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### Defining the restriction operator in nested multigrid FEM

I'm new in the multigrid approach and I'm trying to implement an algorithm from this paper: https://www.researchgate.net/publication/242913687_A_Multigrid_Algorithm_for_the_p-Laplacian I'm stuck with ...
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### Why aren't mortar domain decomposition techniques used as much as schwarts type DD?

Schwartz type domain decomposition techniques require a transmission condition which can be hard to come by. Mortar type techniques enforce continuity with a Lagrange multiplier across domains. Are ...
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### How does the time needed for force propagation increase with the discretization (using symplectic Euler schemes)?

I am trying to model a physical system by (lets say the system is a long deformable object, on which I can apply forces). It can be described by Cosserat Rod theory and discretized, by modelling it ...
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### Does this second-order implicit Runge-Kutta method have a name?

I am studying the time-integration of the following paper, Young, L. C. (1981). A finite-element method for reservoir simulation. Society of Petroleum Engineers Journal, 21(01), 115-128. A copy (PDF)...
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### recommendation on some papers/books about frontal solver used in FEM

I'm reading a program about computational plasticity, this program use frontal solver to solve the program, but I'm not familiar with frontal solver even after reading some papaers, so could you ...
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### error estimate inequalities in finite elements

In finite element textbooks there are error estimate inequalities like $e<~h^p$ or $e<~N^{-p/d}$, where h is the FE length scale, d the # of dimensions, p the FE order, N the # of DOFs. Are ...
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### Appropriate values for fluid-structure interaction model using finite element method in MATLAB

I'm having a program to compute the solution for a fluid-structure interaction model (blood and blood vessel walls) using FEM in MATLAB. The program is running fine but the function that I'm ...
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### Solving systems of advection-diffusion-reaction equations with finite element methods

I have been doing a lot of self-study on numerically solving PDEs so that I can solve system of linear and nonlinear Advection-Diffusion-Reaction (ADR) systems on complex meshes. I have been watching ...
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### PhD in scientific computing to be a scientific programmer

Intro and disclaimer: this question concerns developing a career in Scientific Computing in industry, starting from an (applied) mathematics background, say an MSc. It definitely arises from my ...
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### shape functions of interpolating a piecewise polynomial with continuous 0-th and 1-st derivatives

shape functions are the basis functions that interpolate a function in a subdomain using polynomials. linear interpolation is probably the most convenient approach which results in so-called "...
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I am using FreeFEM++ to simulate the cylindrical waveguide, but no reasonable solution is returned. Here I'm using the 94 GHz light ($\lambda$ = 3.17mm) as input, and radius of the waveguide is 1.27mm....
In snes/tutorials/ex13.c, there is a function SetupPrimalProblem(), which sets up the $f_0$ and $f_1$ in ...