My research focus for a long time was on accuracy verification or fully reliable and efficient error control approaches for the numerical approximations to the evolutionary partial differential equations (PDEs) and ordinary differential equations (ODEs). I have worked on their application to conventional methods (e.g., finite difference and finite element methods in combination with sequential time-stepping discretisations) as well as to the recently introduced isogeometric analysis (IgA) framework combined with the space-time approach (where time is considered as another spatial coordinate).
One of my recent works was concerned with guaranteed and fully computable a posteriori error estimates for evolutionary problems associated with the poroelastic media governed by the quasi-static linear Biot equations (both iterative and monolithic approaches used for semi-discrete approximations obtained by the implicit Euler time-discretization scheme). This led me to the current project, where I concentrate on the chemical reaction solver in Shell’s reservoir simulator. The project involves the development of fast, accurate, and robust computational methods to model thermodynamic and thermophysical properties of fluids and rocks.