PolyDEAL is an open source library which aims to provide building blocks for the developement of Polytopal Discontinuous Galerkin methods, using the Finite Element library deal.II in 2D and 3D. It is ...
In this paper we first review the development of high order ADER finite volume and ADER discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in 1999 by Toro et al. We ...
Abstract: Mathematical models of a complex physicochemical underground coal gasification process involve multidimensional non-linear partial differential equations (PDEs). Therefore, researchers ...
Abstract: A hyperbolic integro-differential equation is considered, as a model problem, where the convolution kernel is assumed to be either smooth or no worse than weakly singular. Well-posedness of ...
Discontinuous Petrov-Galerkin (DPG) methods have emerged as a robust class of finite element techniques designed to enhance stability and accuracy in numerical simulations. By employing discontinuous ...
ABSTRACT: One of the reasons for the great success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved ...
ABSTRACT: The paper is devised to propose finite volume semi-Lagrange scheme for approximating linear and nonlinear hyperbolic conservation laws. Based on the idea of semi-Lagrangian scheme, we ...
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