# Linked Questions

10 questions linked to/from How to model diffusion through a membrane?
16answers
4k views

### Future enhancements for the finite element method

How should the finite element method (FEM) framework in the language be extended to be more useful? With the release of version 12.0 all fundamental FEM solvers (linear, nonlinear, stationary, ...
1answer
5k views

### Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
4answers
969 views

### How to apply different equations to different parts of a geometry in PDE?

I want to solve two coupled partial differential equations on two dimension. There are two variables v and m. The geometry is a ...
2answers
268 views

### 1D mesh generation for PDE solution

I'm trying to solve a system of two PDE that are dependent on time and distance (H[x,t] and P[x,t]). I'm solving the problem using the method of lines but I want to generate myself the mesh and ...
1answer
316 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: $$\partial_t u = \partial_x (D \partial_x u),$$ ...
2answers
356 views

### NDSolve with equation system with unknown functions defined on different domains

Based on @xzczd's excellent answer on solving an equation system with unknown functions defined on different domains, I've tried to apply the same technique to a similar system shown below: Equations: ...
3answers
617 views

### Differential equation with a Heavisidetheta function running for ever

So I'm trying to get the solution of the following differential equation: ...
1answer
134 views

### Trouble with dependent variables in NDSolve while modelling transparent boundary conditions on a quantum graph with Mathematica

I am trying to create a model of plane wave's propagation on a quantum graph(metric graph with a differential operator, Shrodinger operator in my case, along the edges and continuity condition at the ...
1answer
141 views

### Neumann boundary condition ignored

Im trying to solve a system of two PDE (im[t,x] and ia[t,x]) that are dependent on time and distance. I’m using my own anisotropic mesh (thanks to @TimLaska) that is aimed to represent an interface ...
2answers
120 views

### Heat balance in layer coupled via BC

I am trying to solve the heat balance in a 3 layer system in Mathematica 12.0.0. Each layer has different thermal properties. The layers are coupled via the boundary conditions (Neumann type) to ...