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boyfarrell
  • Member for 9 years, 4 months
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55 votes
3 answers
36k views

What are the conceptual differences between the finite element and finite volume method?

33 votes
2 answers
6k views

Strange oscillation when solving the advection equation by finite-difference with fully closed Neumann boundary conditions (reflection at boundaries)

29 votes
2 answers
5k views

Is Crank-Nicolson a stable discretization scheme for Reaction-Diffusion-Advection (convection) equation?

28 votes
1 answer
6k views

Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation

17 votes
2 answers
21k views

Writing the Poisson equation finite-difference matrix with Neumann boundary conditions

17 votes
1 answer
15k views

How should boundary conditions be applied when using finite-volume method?

17 votes
1 answer
1k views

How do you debug numerical code, what could be source of this oscillatory error?

17 votes
1 answer
5k views

When is Newton-Krylov not an appropriate solver?

16 votes
3 answers
1k views

Is variable scaling essential when solving some PDE problems numerically?

15 votes
2 answers
3k views

Is it possible to solve nonlinear PDEs without using Newton-Raphson iteration?

14 votes
1 answer
2k views

Can the advection equation with variable velocity be conservative?

13 votes
3 answers
1k views

What are the basic principles behind generating a moving mesh?

11 votes
3 answers
2k views

How should non-constant coefficients be treated with finite-volume first order upwind scheme?

11 votes
5 answers
507 views

How to deal with complexity in numerical code, for example, when dealing with large Jacobian matrices?

11 votes
3 answers
4k views

Applying Dirichlet boundary conditions to the Poisson equation with finite volume method

9 votes
2 answers
1k views

Peculiar error when solving the Poisson equation on a non-uniform mesh (1D only) finite volume method

9 votes
1 answer
5k views

Are there any numerical advantages in solving symmetric matrix compared to matrices without symmetry?

8 votes
1 answer
726 views

Conservative finite-difference expression for the advection equation

7 votes
1 answer
950 views

Are we free to choose the position of ghost cells on a non-uniform finite-volume mesh?

7 votes
3 answers
3k views

Open boundary conditions with the advection-diffusion equation

7 votes
2 answers
175 views

For a non-linear PDEs should the source term be discretised at $u_j$ or averaged over $(u_{j+1} + u_{j-1})/2$?

6 votes
1 answer
4k views

A simple function for generating a nonuniform mesh in 1D with fixed minimum spacing

6 votes
1 answer
2k views

Trouble implementing Neumann boundary conditions because the ghost points cannot be eliminated

6 votes
2 answers
2k views

Finite-volume method: can Dirichlet boundary conditions be applied to the integral form?

5 votes
2 answers
3k views

Does the finite element method impose any restrictions on the Peclet number for numerical stability?

5 votes
2 answers
570 views

Solving PDE with spatial and temporal derivatives on left hand side

5 votes
1 answer
1k views

Confusion regarding the Adam-Moulton and Backwards Differentiation Formula (BDF) of the VODE solver

5 votes
2 answers
841 views

Are the drift-diffusion equations from semiconductor physics analogous to solving an advection-diffusion problem?

5 votes
1 answer
434 views

Implementing an adaptive discretisation (upwind/central hybrid) for the advection-diffusion equation on a non-uniform mesh

5 votes
2 answers
229 views

Improving the time integration of implicit discretized PDE with a non-linear source term