How to Implement FEM with a Discontinuity in the Exact Solution?

[ageralo]

Homework Statement

Use FEM to solve this problem. The difficulty lies in the fact that the exact solution has a discontinuity in it. From x=[0,0.6) the exact solution u is x⁵/20 - x/20 and from x =(0.6,1] u is sin(x). The problem I'm having is I'm not sure what to do at the jump in my code. I have already set up my matrices Au = f, and it solves it fine given no discontinuity.

u_xx = f

Homework Equations

u(0) = u₀
u(1) = u₁

 

[Ray Vickson]

Homework Statement

Use FEM to solve this problem. The difficulty lies in the fact that the exact solution has a discontinuity in it. From x=[0,0.6) the exact solution u is x⁵/20 - x/20 and from x =(0.6,1] u is sin(x). The problem I'm having is I'm not sure what to do at the jump in my code. I have already set up my matrices Au = f, and it solves it fine given no discontinuity.

u_xx = f

Homework Equations

u(0) = u₀
u(1) = u₁

What is FEM?

RGV

 

[ageralo]

FEM = Finite Element Methods

Here is a pretty good PDF on its basics.

http://www.math.uncc.edu/~shaodeng/TEACHING/math5172/Lectures/Lect_4.PDF