Convergence analysis of a numerical scheme for a tumour growth model

Abstract A one–spatial dimensional tumour growth model Breward et al. ( 2001, 2002, 2003) that consists of three dependent variables space and time is considered. These are volume fraction cells, velocity nutrient concentration. The satisfy a coupled system semilinear advection equation (hyperbolic), simplified linear Stokes (elliptic), diffusion (parabolic) with appropriate conditions on the time–dependent boundary, which governed by an ordinary differential equation. reformulation defined in larger, fixed time–space domain employed to overcome theoretical difficulties related boundary. This reduces complexity removing need explicitly track numerical scheme employs finite method for hyperbolic equation, element elliptic backward Euler time–mass lumped parabolic developed. We establish existence interval $(0,T_{\ast })$ over convergent subsequence approximations can be extracted using compactness techniques. limit any such proved weak solution continuous sense, called threshold solution. Numerical tests justifications support findings conclude paper.