Discontinuous Galerkin Isogeometric Analysis for the biharmonic equation
نویسندگان
چکیده
منابع مشابه
Multipatch Discontinuous Galerkin Isogeometric Analysis
Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get flexibility in the geometrical representation. This multi-patch representation corresponds to a decomposition of the computational domain into non-overlapping sub...
متن کاملMixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation
In this paper, we first split the biharmonic equation !2u = f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v = !u and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation vh of v can easily be eliminated to reduce the discrete problem to a Schur complement sys...
متن کاملDiscontinuous Galerkin Isogeometric Analysis of Elliptic PDEs on Surfaces
The Isogeometric Analysis (IGA) was introduced by Hughes et al. [2005] and has since been developed intensively, see also monograph Cottrell et al. [2009], is a very suitable framework for representing and discretizing Partial Differential Equations (PDEs) on surfaces. We refer the reader to the survey paper by Dziuk and Elliot [2013] where different finite element approaches to the numerical s...
متن کاملA PRIORI ERROR ANALYSIS FOR THE hp-VERSION OF THE DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR THE BIHARMONIC EQUATION
We consider the hp-version of the discontinuous Galerkin finite element approximation of boundary value problems for the biharmonic equation. Our main concern is the a priori error analysis of the method, based on a nonsymmetric bilinear form with interior discontinuity penalization terms. We establish an a priori error bound for the method which is of optimal order with respect to the mesh siz...
متن کاملA Hybridizable and Superconvergent Discontinuous Galerkin Method for Biharmonic Problems
In this paper, we introduce and analyze a new discontinuous Galerkin method for solving the biharmonic problem ∆u = f . The method has two main, distinctive features, namely, it is amenable to an efficient implementation, and it displays new superconvergence properties. Indeed, although the method uses as separate unknowns u, ∇u, ∆u and ∇∆u, the only globally coupled degrees of freedom are thos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2018
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2018.05.001