The ubiquity of semilinear parabolic equations is clear from their numerous applications
ranging from physics and biology to materials and social sciences. In this paper, we …

Convection-diffusion-reaction equations model the conservation of scalar quantities. From
the analytic point of view, solutions of these equations satisfy, under certain conditions …

Solutions to many partial differential equations satisfy certain bounds or constraints. For
example, the density and pressure are positive for equations of fluid dynamics, and in the …

We propose second order accurate discontinuous Galerkin (DG) schemes which satisfy a
strict maximum principle for general nonlinear convection–diffusion equations on …

Simplicial Partitions with Applications to the Finite Element Method Page 1 Springer
Monographs in Mathematics Simplicial Partitions with Applications to the Finite Element …

In this paper we develop a numerical method for pricing American options under regime-
switching model, whose solutions are option buyer indifference prices. The problem is …

In this paper, we propose to apply the parametrized maximum-principle-preserving (MPP)
flux limiter in [T. Xiong, J.-M. Qiu, and Z. Xu, J. Comput. Phys., 252 (2013), pp. 310--331] to …

We present a fully discrete scheme for the numerical approximation of a moving-boundary
problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite …

In this paper, we consider models of cancer migration and invasion, which consist of two
nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of …

The lumped mass method is extended to the surface finite element method for solving the
surface parabolic equations. The main purpose of the proposed method is to overcome the …