# 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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### preconditioner for Laplace "without" boundary values

I'm looking at solving systems with the FEM discretization $$-\int_\Omega (\Delta u) v = \int_\Omega \nabla u \cdot \nabla v - \int_\Gamma (n\cdot\nabla u) v.$$ without applying Dirichlet- or ...
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### Step3 in deal.II - Convergence of the mean

I'm trying to understand the Convergence of the mean part of the Step-3 tutorial in deal.II. The authors say that $\frac{1}{|\Omega|}\int_{\Omega} u_h(x)dx$ converges with $\mathcal{O}(h^2)$, but I ...
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### Finite element method for an equation requiring switch between spectral and temporal domain

Some equations (such as the non-linear schrödinger equation for pulse propagation) are more easily solved in the spectral form, but still need a representation in the temporal domain to calculate ...
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### Parallel In Time with Multigrid

I am trying to solve the linear finite element equation $M\ddot{u}+Ku=F(t)$, where $M$ is the mass matrix ,$K$ the stiffness matrix and $F(t)$ the external load vector, parallel in time using XBraid ...
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### Solution predictors for accelerating convergence in nonlinear FEM

I am looking for the details of commonly-used predictors for accelerating the convergence of iterations using Newton-Raphson scheme for nonlinear problems in FEM. I am looking specifically for static ...
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### How to use FEniCS to calculate the electric field of an isolated charged sphere

Initially I thought that this is the kind of question which ought to have already been answered in the form of an example online, but so far I haven't found one. I will admit that I am very new to ...