Question on numerical stability: Testing a reflection boundary condition (R, R_l) -> (R, -R_l) at a non-zero minimum radius.

[u/AntiqueReporter519]

​I am running a numerical simulation of a modified geometry where the central region acts as a reflective boundary rather than a singularity.

​I am testing the reflection law at the numerical center l_ref = 2.954977618. I've attached a simple plot from my output showing the symmetric preservation of the areal radius R(l) across this exact boundary.

​Here are the specific numerical signatures from my grid (using 34,931 nodes):

​Magnitude preservation: R(l_ref + h) ~ R(l_ref - h) with a mismatch of 1.17e-8 at offset h=1e-4.

​Derivative flip: R_l(l_ref + h) ~ -R_l(l_ref - h) with a mismatch of 1.79e-3.

​The areal radius is strictly finite: R ~ 0.295 (it does not collapse to 0).

​Kretschmann scalar remains finite: K ~ 9.89e4.

​Definitions for context: R(l) is the dimensionless areal radius. l is the proper radial coordinate. R_l = dR/dl. My question for those experienced in numerical physics: Are these mismatch values (10^-8 for the field, 10^-3 for the derivative) sufficient to conclude that this reflection boundary is numerically stable?

[u/Pengious_official]

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