Endre Süli
University of Oxford
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Featured researches published by Endre Süli.
Acta Numerica | 2002
Michael B. Giles; Endre Süli
We give an overview of recent developments concerning the use of adjoint methods in two areas: the a posteriori error analysis of finite element methods for the numerical solution of partial differential equations where the quantity of interest is a functional of the solution, and superconvergent extraction of integral functionals by postprocessing.
SIAM Journal on Numerical Analysis | 2001
Paul Houston; Christoph Schwab; Endre Süli
We consider the hp-version of the discontinuous Galerkin finite element method (DGFEM) for second-order partial differential equations with nonnegative characteristic form. This class of equations includes second-order elliptic and parabolic equations, advection-reaction equations, as well as problems of mixed hyperbolic-elliptic-parabolic type. Our main concern is the error analysis of the method in the absence of streamline-diffusion stabilization. In the hyperbolic case, an hp-optimal error bound is derived; here, we consider only advection-reaction problems which satisfy a certain (standard) positivity condition. In the self-adjoint elliptic case, an error bound that is h-optimal and p-suboptimal by
Numerische Mathematik | 1988
Endre Süli
\frac{1}{2}
SIAM Journal on Numerical Analysis | 1991
Endre Süli
a power of p is obtained. These estimates are then combined to deduce an error bound in the general case. For elementwise analytic solutions the method exhibits exponential rates of convergence under p-refinement. The theoretical results are illustrated by numerical experiments.
SIAM Journal on Numerical Analysis | 1994
Peter Monk; Endre Süli
SummaryThe Lagrange-Galerkin method is a numerical technique for solving convection — dominated diffusion problems, based on combining a special discretisation of the Lagrangian material derivative along particle trajectories with a Galerkin finite element method. We present optimal error estimates for the Lagrange-Galerkin mixed finite element approximation of the Navier-Stokes equations in a velocity/pressure formulation. The method is shown to be nonlinearly stable.
Mathematical Models and Methods in Applied Sciences | 2004
Franco Brezzi; L. D. Marini; Endre Süli
An error analysis of a family of cell-center finite volume schemes for Poisson’s equation on Cartesian product nonuniform meshes in two dimensions is presented. Optimal-order error estimates are derived in the discrete
SIAM Journal on Scientific Computing | 2001
Paul Houston; Endre Süli
H^1
SIAM Journal on Numerical Analysis | 2000
Paul Houston; Christoph Schwab; Endre Süli
norm under minimum smoothness requirements on the exact solution and without any additional assumption on the regularity of the mesh. On quasi-uniform meshes analogous estimates are obtained in the maximum norm.
Mathematics of Computation | 2003
Bernardo Cockburn; Mitchell Luskin; Chi-Wang Shu; Endre Süli
The Yee scheme is the principal finite difference method used in computing time domain solutions of Maxwell’s equations. On a uniform grid the method is easily seen to be second-order convergent in space. This paper shows that the Yee scheme is also second-order convergent on a nonuniform mesh despite the fact that the local truncation error is (nodally) only of first order.
Computer Methods in Applied Mechanics and Engineering | 2000
Paul Houston; Rolf Rannacher; Endre Süli
The main aim of this paper is to highlight that, when dealing with DG methods for linear hyperbolic equations or advection-dominated equations, it is much more convenient to write the upwind numerical flux as the sum of the usual (symmetric) average and a jump penalty. The equivalence of the two ways of writing is certainly well known (see e.g. Ref. 4); yet, it is very widespread not to consider upwinding, for DG methods, as a stabilization procedure, and too often in the literature the upwind form is preferred in proofs. Here, we wish to underline the fact that the combined use of the formalism of Ref. 3 and the jump formulation of upwind terms has several advantages. One of them is, in general, to provide a simpler and more elegant way of proving stability. The second advantage is that the calibration of the penalty parameter to be used in the jump term is left to the user (who can think of taking advantage of this added freedom), and the third is that, if a diffusive term is present, the two jump stabilizations (for the generalized upwinding and for the DG treatment of the diffusive term) are often of identical or very similar form, and this can also be turned to the users advantage.