A compact finite volume method and its extrapolation for elliptic equations with third boundary conditions

Error estimates on a finite volume method for diffusion problems with interface on rectangular grids

“…Many researchers investigated this kind of FVMs, e.g. [8,9,10,11,12,13,14,15,16,17,18,19]. Ewing constructed an immersed finite volume element method (FVEM) on a uniform triangle grid, and presented the optimal error estimate in the energy norm ( [8,9]).…”

“…Luce derived a kind of FVM by using a decomposition technique in [16]. Wang constructed a fourth-order compact FVM and derived some high accuracy post-processing formulas in [17]. Li proved the optimal L 2 error estimate for bilinear and biquadratic FVMs with smooth coefficients under a mesh restriction of h 2parallelogram, respectively ( [18,19]).…”