27,143 research outputs found
eXtended hybridizable discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces
The eXtended hybridizable discontinuous Galerkin (X-HDG) method is developed for the solution of Stokes problems with void or material interfaces. X-HDG is a novel method that combines the hybridizable discontinuous Galerkin (HDG) method with an eXtended finite element strategy, resulting in a high-order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level-set function. For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems. Two-dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X-HDG, with the freedom of computational meshes that do not fit the interfacesPeer ReviewedPostprint (author's final draft
A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations
In this paper the numerical solution of non-autonomous semilinear stochastic
evolution equations driven by an additive Wiener noise is investigated. We
introduce a novel fully discrete numerical approximation that combines a
standard Galerkin finite element method with a randomized Runge-Kutta scheme.
Convergence of the method to the mild solution is proven with respect to the
-norm, . We obtain the same temporal order of
convergence as for Milstein-Galerkin finite element methods but without
imposing any differentiability condition on the nonlinearity. The results are
extended to also incorporate a spectral approximation of the driving Wiener
process. An application to a stochastic partial differential equation is
discussed and illustrated through a numerical experiment.Comment: 31 pages, 1 figur
Intrinsic finite element modeling of a linear membrane shell problem
A Galerkin finite element method for the membrane elasticity problem on a
meshed surface is constructed by using two-dimensional elements extended into
three dimensions. The membrane finite element model is established using the
intrinsic approach suggested by [Delfour and Zol\'esio, A boundary differential
equation for thin shells. J. Differential Equations, 119(2):426--449, 1995]
Optimal L2-error estimates for the semidiscrete Galerkin\ud approximation to a second order linear parabolic initial and\ud boundary value problem with nonsmooth initial data
In this article, we have discussed a priori error estimate for the semidiscrete Galerkin approximation of a general second order parabolic initial and boundary value problem with non-smooth initial data. Our analysis is based on an elementary energy argument without resorting to parabolic duality technique. The proposed technique is also extended to a semidiscrete mixed method for parabolic problems. Optimal L2-error estimate is derived for both cases, when the initial data is in L2
- …