In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar conservation laws with stiff source terms by extending the idea in Zhang and Shu [39]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical...

This paper investigates the use of a special class of strong-stability-preserving (SSP) Runge–Kutta time discretization methods in conjunction with discontinuous Galerkin (DG) finite element spatial discretizatons. The class of SSP methods investigated here is defined by the property that the number of stages s is greater than the order k of the method. From analysis, CFL conditions for the lin...

A posteriori error estimation for conforming, non-conforming and discontinuous finite element schemes are discussed within a single framework. By dealing with three ostensibly different schemes under the same umbrella, the same common underlying principles at work in each case are highlighted leading to a clearer understanding of the issues involved. The ideas are presented in the context of pi...

Consider the problem− 2∆u+u = f with homogeneous Neumann boundary condition in a bounded smooth domain in RN . The whole range 0 < ≤ 1 is treated. The Galerkin finite element method is used on a globally quasi-uniform mesh of size h; the mesh is fixed and independent of . A precise analysis of how the error at each point depends on h and is presented. As an application, first order error estima...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Tiivistelmä (in Finnish) . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Fully discrete discontinuous Galerkin methods with variable meshes in time are developed for the fourth order Cahn-Hilliard equation arising from phase transition in materials science. The methods are formulated and analyzed in both two and three dimensions, and are proved to give optimal order error bounds. This coupled with the flexibility of the methods demonstrates that the proposed discont...

We develop new stabilized mixed finite element methods for Darcy flow. Stability and an a priori error estimate in the ‘‘stability norm’’ are established. A wide variety of convergent finite elements present themselves, unlike the classical Galerkin formulation which requires highly specialized elements. An interesting feature of the formulation is that there are no mesh-dependent parameters. N...

ה ןויעה םוי 35 חשיא לש " מ 0 1 רבוטקואב 013 2 , ןב תטיסרבינוא ןוירוג , ראב עבש , לארשי