14 citations · 23 across the 12 of their papers we have counts for
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Error Estimates of Generic Discretisation of Reaction-Diffusion System with Constraints
Yahya Alnashri
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we der…
Error Estimates for Non Conforming Discretisation of Time-dependent Convection-Diffusion-Reaction Model
Hasan Alzubaidi, Yahya Alnashri
We use a generic framework, namely the gradient discretisation method (GDM), to propose a unified numerical analysis for general time-dependent convection-diffusion-reaction models…
A generic Scheme For the time-dependent Navier-Stokes Equation Coupled With The Heat Equation
Yahya Alnashri
In this work, we study the gradient discretisation method (GDM) of the time-dependent Navier-Stokes equations coupled with the heat equation, where the viscosity depends on the tem…
Generic Numerical Analysis of Stochastic Reaction Diffusion Model with applications in excitable media
Yahya Alnashri, Hasan Alzubaidi
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several…
A new Discrete Analysis Of Fourth Order Elliptic Variational Inequalities
Yahya Alnashri
This paper applies the gradient discretisation method (GDM) for fourth order elliptic variational inequalities. The GDM provides a new formulation of error estimates and a complete…
The gradient discretisation method for the chemical reactions of biochemical systems
Yahya Alnashri, Hasan Alzubaidi
We consider a biochemical model that consists of a system of partial differential equations based on reaction terms and subject to non--homogeneous Dirichlet boundary conditions. T…
A General Error Estimate For Parabolic Variational Inequalities
Yahya Alnashri
The gradient discretisation method (GDM) is a generic framework designed recently, as a discretise in spatial space, to partial differential equations. This paper aims to use the G…
A gradient Discretisation Method For Anisotropic Reaction Diffusion Models with applications to the dynamics of brain tumours
Yahya Alnashri, Hasan Alzubaidi
A gradient discretisation method (GDM), Gradient schemes, Convergence analysis, Existence of weak solutions, Anisotropic reaction diffusion models, Dirichlet and Neumann boundary c…
A gradient discretisation method to analyse numerical schemes for non-linear variational inequalities, application to the seepage problem
Yahya Alnashri, Jerome Droniou
Using the gradient discretisation method (GDM), we provide a complete and unified numerical analysis for non-linear variational inequalities (VIs) based on Leray--Lions operators a…
Gradient schemes for the Signorini and the obstacle problems, and application to hybrid mimetic mixed methods
Yahya Alnashri, Jerome Droniou
Gradient schemes is a framework which enables the unified convergence analysis of many different methods -- such as finite elements (conforming, non-conforming and mixed) and finit…