[PDF] Top 20 Analysis of the discontinuous Galerkin method for elliptic problems on surfaces

... the discontinuous Galerkin (DG) framework to a linear second-order elliptic problem on a compact smooth connected and oriented surface in R 3 ...(IP) method is introduced on a discrete surface ... See full document

... FEM analysis considered in Dziuk [1988] for linear ansatz functions/suface approx- imation), we approximate Γ by a piecewise polynomial discrete surface Γ k h of order k ≥ ... 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

... operator introduced in [17]. The estimates are a generalisation of the a priori error estimates derived in [14] for the surface interior penalty (IP) method, which restricted the analysis to the linear ... See full document

... PDE problems posed on complicated domains which contain local geometrical features in an efficient ...error analysis of the proposed DGCFEM, based on generating a hierarchy of meshes, such that the finest ... See full document

... 3. Construction of composite DGFEMs. In this section we briefly introduce the composite version of the IP DGFEM; for further details, we refer to our recent article [10]. In order to develop the a priori error ... See full document

... direct discontinuous Galerkin method is given in Section ...error analysis and derive computable lower bounds for the constant coefficients in numerical fluxes in order to guarantee the stability ... 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

... fraction method which only mark a fixed percentage of elements at each refinement level can lead to slow convergence of the combined adaptive Newton-Galerkin ... See full document

... numerical method using an implicit rep- resentation of the surface for which we can show a discrete analogue to the global conservation ...solve problems of this form, we are required to consider two ... See full document

... hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem based on the appli- cation of a single step of a ... 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 analysis of discontinuous Galerkin approximations of locally Lipschitz spatial nonlinearities in quasi-linear elliptic and hyperbolic systems, we did not discuss fully discrete ... See full document

... The article is organized as follows. In Section 2, we state the weak formulation of (1.1)–(1.3) and prove its well-posedness. In Section 3 we formulate the interior penalty hp–DGFEM for the numerical approximation of the ... 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

... S i is the area of a triangle. The distribution of the element area for the triangular mesh at hand is shown on Fig. 2. From this distribution, several values of c g have been seleted for the separation threshold whih ... See full document

... The Vlasov-Poisson (1) problem involves a distribution function f = f (t, x, v). Instead of solving a full 2D problem, we reduce to the solution of 1D problems of type (2) through the second-order Strang splitting ... See full document

... new discontinuous Galerkin method with a symmetric principal bilinear form, but in [25] the primal formulation used to establish an a priori error estimate is no longer consistent due to the nature ... See full document

... The aim of this paper is to consider the use of the DG method of Hu and Shu [11] to solve HJ equations using a moving mesh method based on the solution of MMPDEs. The governing equation is transformed to ... See full document

... in [12]. We refer also to the recent papers [13, 19, 20] who work in a finite volume setting. DG methods have been implemented previously for poroelastic wave propagation; we mention [14, 15] who worked in the time ... See full document