6 citations · 6 across the 5 of their papers we have counts for
7 papers
Well-posedness and regularity for seminlinear time-dependent second and fourth order in space equations
Gopikrishnan Chirappurathu Remesan
This article discusses a unified convergence analysis of the semilinear time-dependent equation with $\mathrm{m} \in \…
Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems
Carsten Carstensen, Neela Nataraj, Gopikrishnan C. Remesan +1
A unified framework for fourth-order semilinear problems with trilinear nonlinearity and general source allows for quasi-best approximation with lowest-order finite element methods…
Two-phase model of compressive stress induced on a surrounding hyperelastic medium by an expanding tumour
Gopikrishnan C. Remesan, Jennifer A Flegg, Helen M Byrne
\emph{In vitro} experiments in which tumour cells are seeded in a gelatinous medium, or hydrogel, show how mechanical interactions between tumour cells and the tissue in which they…
Strong bounded variation estimates for the multi-dimensional finite volume approximation of scalar conservation laws and application to a tumour growth model
Gopikrishnan Chirappurathu Remesan
A uniform bounded variation estimate for finite volume approximations of the nonlinear scalar conservation law in two and three…
Numerical solution of a two dimensional tumour growth model with moving boundary
Jerome Droniou, Jennifer A. Flegg, Gopikrishnan C. Remesan
We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A li…
Convergence analysis of a numerical scheme for a tumour growth model
Jerome Droniou, Neela Nataraj, Gopikrishnan Chirappurathu Remesan
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumo…
Numerical solution of the two-phase tumour growth model with moving boundary
Gopikrishnan C. Remesan
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The…