Linked Questions

9
votes
3answers
958 views

How to use Finite elements to solve an initial value ODE with NDSolve?

This is on 11.3, windows 7 I have not used Mathematica FEM much at all. So sorry for this basic question on using it to solve a basic second order initial value ODE. I want to use ...
13
votes
2answers
387 views

Reveal the formal PDE of FiniteElement

When FiniteElement method is used, the differential equations will first be transformed to certain standard form (named as formal PDE in recent FEM document), and ...
7
votes
2answers
4k views

Analytic solution for 1D heat equation

I would like to use Mathematica to solve a simple heat equation model analytically. I have an insulated rod, it's 1 unit long. At x = 0, there is a Neumann boundary condition where the temperature ...
7
votes
3answers
422 views

Wrong solution from multi materials FEM NDSolve

I'm quite new in Mathematica. I have a problem with obtaining the right solution for multi-layer 1D heat transfer problem. It seems that boundary condition not working. Could you advise something? I ...
13
votes
1answer
2k views

NDSolveValue - Heat flux continuity

I'm having some problems with NDSolve and the problem of conduction of heat. Specifically I'm having problems with the continuity of heat flux. First, let me ...
6
votes
1answer
722 views

heat balance solution in two adjacent layers with continuous flux over boundary

I am trying to solve the heat equation for a system made of a cylinder (hot) that is suddenly immersed in a cooling medium (cold). I am doing this using a 1D approximation with single differential ...
9
votes
1answer
393 views

How to handle discontinuity in diffusion coefficient?

I am looking to solve the diffusion equation with a discontinuous jump in the diffusion coefficient. In 1D, the diffusion equation for $u(t,x)$ is: $$ \partial_t u = \partial_x (D \partial_x u), $$ ...
7
votes
1answer
358 views

The rectangular region composed of two triangular regions contains a pde connecting the bc of the first and the second kind

I'm going to solve the Laplacian equation of the electrostatic field, which consists of two triangular regions, a rectangular region, a square, and on the intersection of the two regions of $$y=x$$, ...
2
votes
1answer
298 views

Heat transport in 1d, two different materials at point contact with NDsolve -

I have two materials touching at a point x=0. 1) The first material lies within the interval [-L1, 0], has diffusion constant D1, and the heat conductivity kappa1. Its left end is kept on time ...
3
votes
2answers
353 views

how to fix this PDE numerical solution (NDSolve)

I have the following code: ...
0
votes
1answer
242 views

2D heat conduction/advection through an annulus with Dirichlet Conditions

I want to simulate heat conduction (and advection) through an annulus and its surrounding material in 2D, as illustrated in this mesh: For the heat conduction, I want two Dirichlet boundary ...
2
votes
0answers
107 views

Difficulty setting a time step or stabilizing the transient heat equation

I have been trying to solve the transient heat equation using finite elements. When I set the thermal diffusivity to a realistic number I get instabilities in the solution. It seems that larger ...