Wormhole propagation plays a very important role in the product enhancement of oil and gas reservoir. A new combined hybrid mixed finite element method is proposed to solve incompressible wormhole problem with discontinuous Galerkin procedure, which, algorithm established for pressure equation, while considered concentration then porosity function computed straightly by approximate value concen...

Abstract. We consider a norm-preconditioning approach for the solution of discontinuous Galerkin finite element discretizations of second order PDE with non-negative characteristic form. In particular, we perform an analysis for the general case of discontinuous hp-finite element discretizations. Our solution method is a norm-preconditioned threeterm GMRES routine. We find that for symmetric po...

This work will explore the discontinuous Galerkin finite element method (DG-FEM) for solving acoustic wave equations in heterogeneous material. High order convergence of DG-FEM will be verified by examples. The numerical error using DG-FEM has the same components as using finite-difference method: grid dispersion and misalignment between numerical grids and material interfaces. Both error compo...

In this paper we present an error estimate for the explicit Runge-Kutta discontinuous Galerkin method to solve linear hyperbolic equation in one dimension with discontinuous but piecewise smooth initial data. The discontinuous finite element space is made up of piecewise polynomials of arbitrary degree, and time is advanced by the third order explicit total variation diminishing Runge-Kutta met...

In this paper, we study the convergence and time evolution of the error between the discontinuous Galerkin (DG) finite element solution and the exact solution for conservation laws when upwind fluxes are used. We prove that if we apply piecewise linear polynomials to a linear scalar equation, the DG solution will be superconvergent towards a particular projection of the exact solution. Thus, th...