New L2 error estimates for weighted L2 projections of H1 functions are controlled by the H1 semi-norm except under highly irregular weights such as checkerboard patterns.
Hu, Convergence of the Hiptmair-Xu preconditioner fo r H(curl)-elliptic problems with jump coefficients (ii): Main Results, SIAM Journal on Numerical An alysis, 61(2023), 2434-2459
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New error estimates of the weighted $L^2$ projections
New L2 error estimates for weighted L2 projections of H1 functions are controlled by the H1 semi-norm except under highly irregular weights such as checkerboard patterns.