[PDF] Top 20 hp Version composite discontinuous Galerkin methods for elliptic problems on complicated domains

... PDE problems posed on complicated domains which contain local geometrical features in an efficient ...each composite element the numerical solution is a polynomial; by selecting alternative ... See full document

... as Composite Finite Elements (CFEs), have been developed for the numerical solution of partial differential equations, which are particularly suited to problems characterized by small details in the ... See full document

... the hp–meshes after 7 and 16 adaptive ...the hp–adaptive algorithm increased the degree of the approximating polynomial within the interior part of the domain containing these ... See full document

... of Discontinuous Galerkin (DG) methods date back over 50 years ...DG methods were constructed for elliptic problems based on weakly enforcing Dirichlet boundary conditions; see, ... See full document

... diffusion problems, and to [19,38] for the treatment of strongly monotone quasilinear PDEs, ...for hp–version two-grid DG ...of discontinuous finite element functions by conforming ones, ... See full document

... the hp–version DGFEM ...introduce composite/agglomerated DGFEMs for the numerical approximation of second–order elliptic ...derive hp–version inverse estimates and approximation ... See full document

... the hp version of the three families of Eulerian-Lagrangian mixed discontinuous finite element (MDFE) methods and their equivalent Galerkin versions for the numerical solution of ... See full document

... to problems posed on complicated domains which may contain a huge num- ber of local geometrical features, or ...the composite variant of the discontinuous Galerkin finite element ... See full document

... two-grid hp-version discontinuous Galerkin finite element methods (DGFEMs) for the numerical approximation of strongly monotone quasi-Newtonian fluid flow ...two-grid methods is ... See full document

... so-called Composite DGFEMs; this approach allows for the numerical approximation of partial differen- tial equations posed on complicated domains which contain ‘small’ geometrical fea- tures, or ... See full document

... an hp–version DGFEM of interior penalty (IP) type for linear elliptic problems on meshes consisting of d–dimensional polytopic elements ... See full document

... control problems in [, ...the hp-version of the finite element method for optimal control prob- lems is rather ...by elliptic equations, the authors have derived a posteriori error estimates ... See full document

... two methods that we selected from literature for further study, make a fundamentally different choice for this ...both methods in detail for a generalized Poisson ... See full document

... In Chapter 5, which is based on work we have done in Dedner and Madhavan [2014a], we derive a dual weighted residual-based a posteriori error estimate for the surface IP method considered in Chapter 4, restricting ... See full document

... parabolic problems are presented in [34], for 2D elliptic problems in [1, 19, 20], and for 2D compressible nonlinear Navier–Stokes equations in ...nonlinear problems this is even more ... See full document

... Here we compare different approaches for the indicator used to set the local polynomial degree. In the following we always use the implicit method with τ = 5, h-adaptivity with a maximum level of three and also a maximum ... See full document

... The Warwick Research Archive Portal (WRAP) makes this work of researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the ... See full document

... linear elliptic problems and partial differential equations with nonnegative characteristic ...form. Discontinuous Galerkin finite element methods were introduced in the early 1970s for ... See full document

... extended version of the presentation for the International Conference on Computational Science ICCS 2012 [Calo ...Automatic hp Adaptivity we introduce an overview of the self- adaptive goal-oriented ...the ... See full document

... In the nonlinear setting, assuming a Newton-type iteration is exploited to solve the underlying system of nonlinear equations stemming from the given FEM employed, the general strategy of assembly of the resulting ... See full document