# Questions tagged [boundary-conditions]

For questions regarding the choice and/or appropriateness of conditions necessary to model a particular phenomenon with a partial differential equations.

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### “This DAE appears to be of index greater than 1” daeic12 (line76) error code

Hi I am trying to solve a set of pde converted into ODE and DAE using central finite difference method. I have used the MATLAB 'solve' command to determine the coefficients of fictitious nodes for ...
89 views

### 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 ...
34 views

### Numerical simulation for a bounded process. Is slight deviation a “normal” fact?

Suppose I have to numerically simulate a process $\{y_t\}$ such that $y_t\geq0$ $\forall t\in\mathbb{N}$, with $t$ denoting time-step. Let's suppose I use MonteCarlo with $\mathscr{N}$ simulation ...
29 views

### At what l/d ratio will a frame element start to behave as a shell element?

I'm working in ETABS. There are few columns of dimension 300mmx1400mm. The height of building is 36.6 meter above ground level and the dimension of building is 26mx68m. I'm getting the time period of ...
59 views

### COMSOL Circularl polarization

I'm having some problems trying to implement circularly polarized light in COMSOL Muliphysics. For a isotropic homogenous media, I've obtained without problems the TE and TM reflectance curves. ...
74 views

### Applying boundary Conditions on FEM

I have a partial differential equatons as shown below. $$\dfrac{d}{dx}((1+x)\dfrac{du(x)}{dx})=0$$ With the following boundary conditions. $$u(0)=0, u(3)=10$$ To solve it using FEM, I multiplied the ...
40 views

### Boundary Conditions for Continuum Mechanics

If I'm given some sort of shape and there is a displacement given but there are no external forces acting on the body, do I still need to write down the traction free boundary conditions or will there ...
68 views

### Pressure boundary conditions in Stokes Equation in 2D

I am solving the steady-state incompressible Stokes equations in 2D: $$\frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} = 0,$$ \mu\left[\...
63 views

### A non linear ode with boundary conditions at infinity

I want to solve the non-linear ODE $$\frac{d^2}{dx^2}y=a(y+y^3)$$ With the boundary conditions that $$\lim_{x\to \pm \infty} y(x) =0$$ I am not aware of any analytical method for solving this kind ...
47 views

### Neumann boundary conditions on arbitrary surface for finite difference diffusion

I am facing the following problem, formulated in practical terms: I have a region $\Omega$ in two or three dimensions, represented as a binary mask, and an initial density $u_0$ within that region ...
I'm discretizing the following Poisson equation using FVM where the domain $\Omega$ of the solution is a regular hexagon of side $1$ centered about the origin. $$\Delta u =k,\text{ k constant}\\ \... 1answer 310 views ### Proving solution existence and uniqueness of the Helmholtz equation with Robin boundary conditions with complex coefficients I am trying to solve the Helmholtz equation with Robin boundary conditions with complex coefficients and the weak formulation$$ \iint_\limits\Omega\nabla p_0(x,y)\nabla\left(\overline{v(x,y)}\right)...
I am dealing with a highly nonlinear system of two PDEs. I already have a code to solve the system in case of Dirichlet boundary conditions. The explicit system is:  \begin{eqnarray*} \partial_{t}u ...