We consider variational inequalities with different trial and test spaces and a possibly non-coercive bilinear form. Well-posedness is shown under general conditions that are e.g. valid for the space-time variational formulation of parabolic variational inequalities. Moreover, we prove an estimate for the error of a Petrov-Galerkin approximation in terms of the residual. For parabolic variation...

We consider a space-time variational formulation for linear parabolic partial differential equations. We introduce an associated Petrov-Galerkin truth finite element discretization with favorable discrete inf-sup constant βδ: βδ is bounded from below by unity for the heat equation; βδ grows only linearly in time for non-coercive (asymptotically stable) convection operators. The latter in turn p...

A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtai...

Isogeometric Analysis (IGA), in combination with the Streamline Upwind Petrov– Galerkin (SUPG) stabilization, is studied for the discretization of steady-state convection-diffusion equations. Numerical results obtained for the Hemker problem are compared with results computed with the SUPG finite element method of the same order. Using an appropriate parameterization for IGA, the computed solut...

D. Gall, M. Städele, K. Järrendahl, I. Petrov, P. Desjardins, R. T. Haasch, T.-Y. Lee, and J. E. Greene Materials Science Department and the Frederick Seitz Materials Research Laboratory, University of Illinois, 104 South Goodwin, Urbana, Illinois 61801 Beckman Institute, University of Illinois, 405 North Mathews Avenue, Urbana, Illinois 61801 Department of Physics, Linköping University, SE-581...

Under general hypotheses on the target set S and the dynamics of the system, we show that the minimal time function TS(·) is a proximal solution to the Hamilton–Jacobi equation. Uniqueness results are obtained with two different kinds of boundary conditions. A new propagation result is proven, and as an application, we give necessary and sufficient conditions for TS(·) to be Lipschitz continuou...

E. G. Petrov,1 V. May,2 and P. Hänggi3 1Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Metrologichna Street, 14-b, UA-03143 Kiev, Ukraine 2Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany 3Institut für Physik, Universität Augsburg, D-86135 Augsburg, Germany Received 7 October 2005; revised manuscript received 2...

The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan [15, 17] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general—though there are some results for Poisson, e.g.—is how best to precondition the DPG system matrix, so that iterative solvers ...

In this article, four Part-of-Speech (PoS) taggers for Spanish are compared. The evaluation has been carried out without prior training or tuning of the PoS taggers. To allow for a comparison across PoS taggers, their tagsets have been mapped to the universal PoS tagset (Petrov, Das, and McDonald, 2012). The PoS taggers have also been compared as regards the information they provide and how the...

This article evaluates the integration of data extracted from a syntactic lexicon, namely the Lexicon-Grammar, into several probabilistic parsers for French. We show that by modifying the Part-ofSpeech tags of verbs and verbal nouns of a treebank, we obtain accurate performances with a parser based on Probabilistic Context-Free Grammars (Petrov et al., 2006) and a discriminative parser based on...