[PDF] Top 20 A hybridizable direct discontinuous Galerkin method for elliptic problems

... the discontinuous Galerkin method (DGM) has been extensively studied by lots of researchers on various problems since it was first introduced by Reed and Hill ...for elliptic ... See full document

... in the interior penalty DG scheme (19), cf. (20), and Λ = 0.5 in Algorithm 5.1, cf. [5]. Throughout this section we shall compare the performance of the proposed hp–adaptive refinement strategy with the corresponding ... See full document

... to problems characterized by small details in the computational domain or micro-structures; see, for example, [11, 10], for ...element method, with the basis function of the CFE being constructed as ... See full document

... compact discontinuous Galerkin 2 (CDG2) method, for solving nonlinear convection-diffusion problems together with a detailed comparison to other well-accepted DG ...CDG2 method is ... See full document

... the direct simulation Monte Carlo method [2] that uses a collection of particles to mimic the molecular behavior stochastically, and the other is the deterministic method, which relies on the ... See full document

... the Discontinuous Galerkin Finite Element Method (DGFEM, for short) can be traced back almost half a century ago to the work undertaken on the weak enforcement of Dirichlet boundary conditions for ... See full document

... for elliptic problems and their error analysis have been successfully applied to problems on surfaces via the intrinsic approach in ...parabolic problems [19] as well as evolving surfaces ... See full document

... computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A ... See full document

... the method for second-order linear elliptic problems and partial differential equations with nonnegative characteristic ...form. Discontinuous Galerkin finite element methods were ... See full document

... of equations is highly sparse, in which only face unknowns that involve in two adjacent triangles are coupled at each row. The system could be solved by robust direct solver for sparse unsymmetrical linear ... See full document

... hyperbolic, elliptic and parabolic PDEs arising from a wide range of ...dominated problems, and less restriction on grid structure and refinement as well as on the choice of basis ...of discontinuous ... See full document

... The structure of this article is as follows. In Section 2, we introduce the model problem and state the necessary assumptions on the computational domain Ω. Sec- tion 3 introduces the composite finite element spaces ... See full document

... The discretization of (6.1) is based on employing the standard upwind DGFEM for the treatment of the advection operator, cf. [25], for example, together with the (symmetric) version of the IP DGFEM for numerical ... See full document

... First, in Figure 6, we can observe the good behavior of the present method compared to BSL. As the degree increases, we observe that the L 2 -norm is becoming closer and closer to that of BSL which is well known ... See full document

... We introduce and analyze a new mixed discontinuous Galerkin method for approximation of an electric field. We carry out its error analysis and prove an error estimate that is optimal in the mesh size. ... See full document

... In order to compare our semi-implicit approach to the schemes given in [, ] and [], we set the parameter values c = ., x = ., ε = μ = .. The run of the algorithm is carried out up to time T = . over the ... See full document

... (IP) discontinuous Galerkin finite element method (DGFEM), based on employing a single step of a Newton solver on the finer space, ...quasilinear elliptic boundary value ... See full document

... of the E z omponent at a seleted point are ompared on Fig. 10. Performane results for the simulations based on the hybrid expliit-impliit DGTD- P 1 method are summarized in T ab. 4. The simulation using the fully ... See full document

... The rest of this paper is as follows. In Section , some notations and auxiliary results are introduced, which will be used later in this paper. In Section , the DG method for ZK equation is presented, and a ... See full document

... Keywords Discontinuous Galerkin method; Two-layer shallow water equations; Finite element; Lock-exchange hydraulics... INTRODUCTION During the last decades partial differential equations[r] ... See full document