How to compute the sum of jump errors on edges in DG

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1

Hello, everyone.

Recently, I am studying the DG methods to solve the Stokes equation. The computation of L2 error, H1error and Diverror is OK, but I cannot find a simple operation to compute the jump error.

The following code is to computate the L2 error:

exactux = x
exactuy = -y
ux_num = gfu.components[0]
uy_num = gfu.components[1]
uL2err = sqrt(Integrate((ux_num-exactux)(ux_num-exactux)+ (uy_num-exactuy)(uy_num-exactuy), mesh))

Please help me! How to code for jump error \Sigma||[uh]|| on all edges?

2

Hi Younghigh,

a quick try of computing the jump ||[\nabla u_h \cdot n]|| via

Integrate((grad(gfu)-grad(gfu).Other())*n*dx(skeleton=True), mesh)

led to the exception

netgen.libngpy._meshing.NgException: other mir not set, pls report to developers.

But with the exact solution at hand the following code should do the job (might not work for older NGSolve versions)

Integrate( (gfu-u_ex)**2*dx(element_boundary=True), mesh)

Note, that you get two values at each inner edge as a loop over elements and then over each element boundary is done.

Best
Michael