# 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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### Thermo Hydraulic Mechanical modeling of energy wall slab in camsol multiphysics

I am currently working on a complex simulation project involving an energy wall slab, and I need assistance in accurately modeling and validating it using COMSOL Multiphysics. Here are the details of ...
1 vote
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### Any FEM book recommendations that focus on stability and proofs on error bounds?

Everything from descrete stability proofs for steady state and time dependent problems. energy stability, stability of mixed methods, nonlinear problems, vector valued problems in fluid/structural/EM, ...
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1 vote
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### Getting singular matrices for lid driven cavity problem

I was trying to solve the lid driven cavity problem using the galerkin method with SUPG stabilization. I was using GMRES method as my solver and I am also getting a solution. And the solution looks ...
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### Lumped (diagonal) vs. consistent (non-diagonal, symmetric) mass matrix in Nastran

I've been tinkering with DMAP to explore the procedure followed by Nastran when solving a complex modes analysis. I've reached a passage I cannot understand: at some point Nastran formulated what it ...
1 vote
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### Immersed Boundary FEM reference recommendation

I want to do some Fluid-Structure Interaction using the Immersed Boundary FEM. Could you please recommend some books or lecture notes on it?
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### What do diagonal (DOF-to-self) terms of stiffness matrix physically mean?

I am used to interpreting each entry of a solid mechanic system's stiffness matrix as a 1D (linear or angular) spring joining one DOF (column index) to another (row index). But this interpretation ...
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### Can finite element exterior calculus be used for the proof of discrete stability?

I've heard about Finite Element Exterior Calculus (FEEC) and its applications in numerical simulations, but can FEEC be utilised to prove discrete stability in computational methods? If so, can the ...
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1 vote
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### How to constraint the tangential gradient on a boundary in FEniCS?

The problem I'm considering is a 2D scalar PDE. The domain $\Omega$ is a disk with two holes $\partial\Omega_1$ and $\partial\Omega_2$ and an external boundary $\partial\Omega_0$. The PDE and boundary ...
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### Gradient of field computed using FEM (L2 Projection)

From my understanding, in the finite element context, an L2 projection can be formulated as the following linear system: $$M\ \phi = \beta$$ where $M$ is the mass matrix, $\phi$ the resulting ...
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### Computational efficiency of Galerkin projection in AMG

I have been using recently AMG as preconditioner for CG with several meshes for simple elliptic problems discretised with linear elements on "complicated" three dimensional geometries and I ...
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### Computing Tangential Derivative using the Dirichlet value

Let $\Gamma$ be a smooth boundary of a domain $\Omega$. Let $u = g$ on $\Gamma$. How can I compute the tangential derivative of the function $u$ using the information that $u = g$ on $\Gamma$? Please ...
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### "Cleanest, most professional" approach to implement a finite differences scheme in dimension greater than two

Coding a finite difference algorithm in 1D does not require a complex mesh. In higher dimensions, you would need a mesh and its connectivity graph to compute the differential operators. Finite ...
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