In this thesis, a high-order finite element scheme, based upon the Discontinuous Galerkin (DG) method, is introduced to solve oneand two-dimensional Elastohydrodynamic Lubrication (EHL) problems (line contact and point contact). This thesis provides an introduction to elastohydrodynamic lubrication, including some history, and a description of the underlying mathematical model which is based up...

We present a high-order entropy stable discontinuous Galerkin (ESDG) method for the two dimensional shallow water equations (SWE) on curved triangular meshes. The presented scheme preserves semi-discrete inequality and remains well-balanced continuous bathymetry profiles. provide numerical experiments which confirm accuracy theoretical properties of scheme, compare to an based simplicial summat...

This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equations. The solutions to such equations often exhibit solitary wave and local structures, which make adaptivity essential in improving the simulation efficiency. Our uses ultra-weak discontinuous Galerkin (DG) formulation belongs framework of multiresolution schemes. Various numerical experiments are presented...

This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite elementmethod (DG-FEM) and theH(curl)-conforming FEM. For the spatial discretisation, hierarchic H(curl)-conforming basis functions are used up to polynomial order p = 3 over tetrahedralmeshes, meaning fourth-order convergence ra...

Nishikawa (2007) proposed to reformulate the classical Poisson equation as a steady state problem for linear hyperbolic system. This results in optimal error estimates both solution of elliptic and its gradient. However, it prevents application well-known solvers problems. We show connections discontinuous Galerkin (DG) method analyzed by Cockburn, Guzm\'an, Wang (2009) that is very difficult i...

In this paper we develop a family of arbitrarily high-order non-oscillatory hybrid Discontinuous Galerkin(DG)-Finite Volume(FV) schemes for mixed-element unstructured meshes. Their key ingredient is switch between DG method and FV based on the CWENOZ scheme when invalid solutions are detected by troubled cell indicator checking unlimited solution. Therefore, high order accuracy offered preserve...