622 research outputs found
An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations
We present and analyze a new embedded--hybridized discontinuous Galerkin
finite element method for the Stokes problem. The method has the attractive
properties of full hybridized methods, namely an -conforming
velocity field, pointwise satisfaction of the continuity equation and \emph{a
priori} error estimates for the velocity that are independent of the pressure.
The embedded--hybridized formulation has advantages over a full hybridized
formulation in that it has fewer global degrees-of-freedom for a given mesh and
the algebraic structure of the resulting linear system is better suited to fast
iterative solvers. The analysis results are supported by a range of numerical
examples that demonstrate rates of convergence, and which show computational
efficiency gains over a full hybridized formulation
A Frame Work for the Error Analysis of Discontinuous Finite Element Methods for Elliptic Optimal Control Problems and Applications to IP methods
In this article, an abstract framework for the error analysis of
discontinuous Galerkin methods for control constrained optimal control problems
is developed. The analysis establishes the best approximation result from a
priori analysis point of view and delivers reliable and efficient a posteriori
error estimators. The results are applicable to a variety of problems just
under the minimal regularity possessed by the well-posed ness of the problem.
Subsequently, applications of interior penalty methods for a boundary
control problem as well as a distributed control problem governed by the
biharmonic equation subject to simply supported boundary conditions are
discussed through the abstract analysis. Numerical experiments illustrate the
theoretical findings. Finally, we also discuss the variational discontinuous
discretization method (without discretizing the control) and its corresponding
error estimates.Comment: 23 pages, 5 figures, 1 tabl
An A Posteriori Error Indicator for Discontinuous Galerkin Approximations of Fourth Order Elliptic Problems
We introduce a residual-based a posteriori error indicator for discontinuous Galerkin discretizations of the biharmonic equation with essential boundary conditions. We show that the indicator is both reliable and efficient with respect to the approximation error measured in terms of a natural energy norm, under minimal regularity assumptions. We validate the performance of the indicator within an adaptive mesh refinement procedure and show its asymptotic exactness for a range of test problems
- …