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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Shape regularity in higher dimensions

In Finite Element theory, and other methods in scientific computing for PDEs, one uses meshes which fulfill several regularity criteria, many of them being equivalent. It is of interest to have ...
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Reference implementation of Nédélec-Elements

Does anybody know of an implementation of Nédélec elements that does not come along with a huge bulk of additional software? Is there a small library written in a language like Python, Matlab, or ...
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2answers
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Which libraries have good implementations of Basis splines?

I'm looking to use the finite element method with B-splines as my function basis. Which C/C++ libraries have good B-spline support? Specifically, I'm looking for an implementation of a stable ...
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1answer
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How to derive the Weak Formulation of a Partial Differential Equation for Finite Element Method?

I have taken a basic introduction to Finite Element Method, which did not emphasize a sophisticated understanding of a 'weak formulation'. I understand that with the galerkin method, we multiply both ...
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1answer
315 views

What are the possible numerical schemes for a diffusion equation with a nonlinear reaction term?

For some simple convex domain $\Omega$ in 2D, we have some $u(x)$ satisfying the following equation: $$ -\mathrm{div}(A\nabla u)+cu^n = f $$ with certain Dirichlet and/or Neumann boundary conditions....
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1answer
239 views

Quadrature rules, methodologies, and references

There is at least one quite comprehensive encyclopaedia of quadrature rules that doesn't seem to have been updated in quite a while and has restricted access. This source refers to several classical ...
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0answers
475 views

How to do FEM in sector elements?

Suppose we have an element in the polar coordinate as $0\leq r\leq 1$, $0\leq\theta\leq \alpha$. What are the correct basis functions in this element? For this kind of mesh, there are a lot of ...
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2answers
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Are 8 Gauss points required for second order hexahedral finite elements?

Is it possible to get second order accuracy for hexahedral finite elements with fewer than 8 Gauss points without introducing unphysical modes? A single central Gauss point introduces an unphysical ...
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2answers
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Solution oscillations with a small timestep in backward Euler

I am using backward Euler in a FEM scheme for a convection-diffusion problem. On a given mesh, I can take arbitrarily large time steps, as expected. But if I decrease time step, at some point it will ...
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2answers
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Looking for a library or algorithms to perfom clipping 3D unstructured meshes by a set of surfaces

We have a 3D (volume) unstructured, possibly hybrid, degenerative irregular mesh data structure that we are capable of generating (mostly composed of hexahedra and general polyhedra, using a mix of ...
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1answer
668 views

What numerical quadrature to choose to integrate a function with singularities?

For example, I would like to numerically compute the $L^2$-norm of $\displaystyle u = \frac{1}{(x^2+y^2+z^2)^{1/3}}$ in some domain that includes zero, I tried Gauss quadrature and it fails, it is ...
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2answers
202 views

Is there one general approach to build a projection methods for different problems?

My question is probably going to be too general to answer it with a couple words. Could you please suggest a good reading in that case. Projection methods are used to reduce size of the solution space ...
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5answers
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What are criteria to choose between finite-differences and finite-elements

I am used to thinking of finite-differences as a special case of finite-elements, on a very constrained grid. So what are the conditions on how to choose between Finite Difference Method (FDM) and ...
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Introductions to hp-FEM

do you know good introductions into or surveys $hp$-adaptive finite elements? In particular I do not know how the heuristics for choosing spatial refinement or increased polynomial degree are ...
13
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1answer
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What are possible methods to solve compressible Euler equations

I would like to write my own solver for compressible Euler equations, and most importantly I want it to work robustly in all situations. I would like it to be FE based (DG is ok). What are the ...
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2answers
692 views

Coupling FEM DG methods to Riemann solvers

Are there any good papers and or codes that couple discontinuous galerkin finite element solvers with Riemann solvers? I need to explore coupling elliptic and hyperbolic problems but most splitting ...
13
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1answer
435 views

What spatial discretizations work for incompressible flow with anisotropic boundary meshes?

High Reynolds number flows produce very thin boundary layers. If wall resolution is used in Large Eddy Simulation, the aspect ratio may be on the order of $10^6$. Many methods become unstable in this ...

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