Uniformly Stable Mixed Hp-finite Elements on Multilevel Adaptive Grids with Hanging Nodes
نویسندگان
چکیده
We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous Pr−1-elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree. Mathematics Subject Classification. 65N30, 65N35, 76D07. Received January 10, 2007. Revised October 2, 2007. Published online April 1st, 2008.
منابع مشابه
Adaptive hp-FEM with Arbitrary-Level Hanging Nodes for Maxwell’s Equations
Adaptive higher-order finite element methods (hp-FEM) are well known for their potential of exceptionally fast (exponential) convergence. However, most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms. This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level...
متن کاملOn the Inf-sup Condition for Higher Order Mixed Fem on Meshes with Hanging Nodes
We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous Pr−1-elements for the pressure where the order r can vary from element to element between 2 and a fixed bound r∗. We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes ...
متن کاملThe hp-multigrid method applied to hp-adaptive refinement of triangular grids
Recently the hp version of the finite element method, in which adaptivity occurs in both the size, h, of the elements and in the order, p, of the approximating piecewise polynomials, has received increasing attention. It is desirable to combine this optimal order discretization method with an optimal order algebraic solution method, such as multigrid. An intriguing notion is to use the values o...
متن کاملhp-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems
We devise and study experimentally adaptive strategies driven by a posteriori error estimates to select automatically both the space mesh and the polynomial degree in the numerical approximation of diffusion equations in two space dimensions. The adaptation is based on equilibrated flux estimates. These estimates are presented here for inhomogeneous Dirichlet and Neumann boundary conditions, fo...
متن کاملAdaptive Unstructured Grid Generation Scheme for Solution of the Heat Equation
An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008