# Tag Info

Accepted

### What is the general idea of Nitsche's method in numerical analysis?

Nitsche's method is related to discontinuous Galerkin methods (indeed, as Wolfgang points out, it is a precursor to these methods), and can be derived in a similar fashion. Let's consider the simplest ...
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### How to efficiently implement Dirichlet boundary conditions in global sparse finite element stiffnes matrices

In deal.II (http://www.dealii.org -- disclaimer: I'm one of the principal authors of that library), we do eliminate whole rows and columns, and it is not too expensive overall. The trick is to use the ...
• 50.7k

### Periodic boundary condition for the heat equation in ]0,1[

The best way to do this is (as you said) to just use the definition of periodic boundary conditions and set up your equations correctly from the start using the fact that $u(0)=u(1)$. In fact, even ...
• 4,521
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### How do I simulate an open end?

The problem you describe, how to prescribe non-reflecting or absorbing boundary conditions when solving partial differential equations (PDE) has been extensively studied. For complex (e.g. nonlinear) ...
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### How to solve a second order differential equation (diffusion) with boundary conditions using Python

I have found that I must keep the value of dt near dx or the results become unstable This behavior you have noticed is known as the Courant–Friedrichs–Lewy (CFL) condition. Indeed, there are ...
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### FEM: Possible to have boundary conditions "inside" the domain?

The solution of the equation you are looking for is in the space $H^1$ of functions that have one weak derivative, but in 2d and 3d, this does not imply that the solution is in fact continuous. As a ...
• 50.7k
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### Transparent boundary conditions for finite element simulation of TDSE

Kirill's answer is a good method but it is hampered that the fact that you need to tune it to a specific range in energy, so it is not appropriate if you have a broad-band wavepacket you need to ...
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### Symmetric boundary condition

For the sake of simplicity let me slightly change your notation. Let $u, v, w$ be the components in the $x, y, z$ directions of a true (polar) vector, and $y=0$ the symmetry plane. For a true vector, ...
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• 861
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### How to apply non zero Dirichlet boundary condition in finite elements?

Consider the fact that your linear system can be broken up into two parts: the equations that correspond to the known Dirichlet dofs, and the equations that correspond to the unknown dofs. For the ...
• 1,522
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### FEM current toy problem

The formulation of this problem is tricky. Here is what you have in your original post: Find $h \in L^2(\partial D)$ such that for any $w \in H^{\frac 1 2}(\partial D)$,  \int_{\partial D} hw \,...
• 50.7k
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### Traction -> stress; stress->displacement gradient

In short, no. Neumann boundary conditions should be specified in terms of traction. This is clear when you move from a strong-form statement of the boundary value problem to a weak-form. Strong form: ...
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### Transparent boundary conditions for finite element simulation of TDSE

In the literature these boundary conditions go by the name of absorbing boundary conditions (or nonreflecting, open, radiation, invisible, far-field), and this is a well-known topic. One clear ...
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### GMRES: Making the matrix square without solving for boundaries

It seems that you are referring to the fluxes that occur at the edge of your domain. Since these are typically known quantities enforced by your boundary conditions, there is no need to solve for ...
• 4,521
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### What are acceptable boundary conditions for porous media flow?

The velocity $\mathbf u$ is in $H^1$, so imposing all or some components of the velocity as boundary conditions is allowed. This includes no-slip or tangential flow boundary conditions. However, from ...
• 50.7k
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### Boundary condition for Pressure in Navier-Stokes equation

When we say that the pressure is only defined "up to a constant", what we mean is this: If $u,p$ is a solution to the Navier-Stokes equations, then $u,p+c$ for any constant $c$ is also a solution. In ...
• 50.7k