[Fishy]

Hi all,

I am trying to solve the diffusion equation using an implicit centred approximation to the second derivative for space and an Euler backward scheme in time. I have implemented a Dirichlet boundary condition one end and would like to use a Neumann boundary condition at the other end. If I choose a backward difference approximation for du/dx, will this incompatibility of the order of delta x (since the centred scheme is order of delta x square and the backward difference of the Neumann boundary condition is order of delta x) affect my errors in anyway as I decrease the discretization and if so, why?

[FMDenaro]

Originally Posted by Fishy

Hi all,

I am trying to solve the diffusion equation using an implicit centred approximation to the second derivative for space and an Euler backward scheme in time. I have implemented a Dirichlet boundary condition one end and would like to use a Neumann boundary condition at the other end. If I choose a backward difference approximation for du/dx, will this incompatibility of the order of delta x (since the centred scheme is order of delta x square and the backward difference of the Neumann boundary condition is order of delta x) affect my errors in anyway as I decrease the discretization and if so, why?

Yes, if you consider the discretization error it will decrease at O(h) near the boundary. You can check that by using the max norm of the error and saving the nodes i,j of the max error.