Linked Questions

103 votes
17 answers
5k 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, ...
user21's user avatar
  • 39.8k
16 votes
3 answers
591 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 ...
xzczd's user avatar
  • 66.2k
4 votes
2 answers
726 views

Dirichlet Condition at Infinity

I have the following system of diffusion equations with these boundary conditions. The second condition is a Dirichlet condition at x approaching infinity. How do I implement that? I've tried ...
Walser's user avatar
  • 351
4 votes
2 answers
564 views

Using Neumann boundary conditions for the wave equation

I have the following code to solve the wave equation in 2D: ...
AccidentalTaylorExpansion's user avatar
2 votes
2 answers
814 views

What causes the warning "The dependent variable in the boundary condition needs to be linear" when using NDSolve?

V 12.1.1 on windows 10 Why the following works ...
Nasser's user avatar
  • 144k
7 votes
1 answer
306 views

1D-waveequation with absorbing boundary condition: FEM solution?

I try to simulate the special absorbing(?) boundary condition `Derivative[1, 0][y][1, t] + Derivative[0, 1 ][y][1, t] == 0` which only allows energy flow in ...
Ulrich Neumann's user avatar
5 votes
1 answer
285 views

Gradient of the numerical solution of a PDE

Solving the following PDE, defined in the same domain of a previous question: ...
umby's user avatar
  • 585
3 votes
1 answer
284 views

Semi-classical approximation of modified Schrodinger's equation on a sphere leads to ndsz warning

I know this error is very common. I checked out a good number of proposed solutions to this problem, but unfortunately, none of them helped in my case. I would appreciate any help or hints on how to ...
Po_oya's user avatar
  • 33
1 vote
1 answer
133 views

Periodic boundary condition conflicts with DirichletCondition?

I want to solve a simple diffuse equation in a cylinder. $\nabla\cdot(\hat{c}\nabla\rho_P)=0$ $\rho_P(x,y,\theta)==0,\sqrt{x^2+y^2}=R$ $\rho_P(0,0,\theta)==1,\sqrt{x^2+y^2}=0$ $\rho_P(x,y,2\pi)=\rho_P(...
江蛮子's user avatar
2 votes
0 answers
93 views

System of PDEs with coupled Neumann BC--how to use NeumannValue?

I have the following system of PDEs for functions $u_1,u_2$ in a region $\Omega\subset\mathbb R^2$: $$ \begin{cases} 2\partial_{xx}u_1+\partial_{yy}u_1+\partial_{xy}u_2-u_1=f_1 & (x,y)\in\Omega\\ \...
Plutoro's user avatar
  • 226