1,018 research outputs found
An adaptive algorithm for the Crank–Nicolson scheme applied to a time-dependent convection–diffusion problem
AbstractAn a posteriori upper bound is derived for the nonstationary convection–diffusion problem using the Crank–Nicolson scheme and continuous, piecewise linear stabilized finite elements with large aspect ratio. Following Lozinski et al. (2009) [13], a quadratic time reconstruction is used.A space and time adaptive algorithm is developed to ensure the control of the relative error in the L2(H1) norm. Numerical experiments illustrating the efficiency of this approach are reported; it is shown that the error indicator is of optimal order with respect to both the mesh size and the time step, even in the convection dominated regime and in the presence of boundary layers
Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements
This paper deals with pricing of European and American options, when the
underlying asset price follows Heston model, via the interior penalty
discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM
space discretization with Rannacher smoothing as time integrator with nonsmooth
initial and boundary conditions are illustrated for European vanilla options,
digital call and American put options. The convection dominated Heston model
for vanishing volatility is efficiently solved utilizing the adaptive dGFEM.
For fast solution of the linear complementary problem of the American options,
a projected successive over relaxation (PSOR) method is developed with the norm
preconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option
pricing by conducting comparison analysis with other methods and numerical
experiments
Three-dimensional finite element modelling of stack pollutant emissions
In this paper we propose a finite element method approach formodelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. The methodology is used to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain).Peer ReviewedPostprint (published version
Adaptive time step control for higher order variational time discretizations applied to convection-diffusion equations
Higher order variational time stepping schemes allow an efficient post-processing for computing a higher order solution. This paper presents an adaptive algorithm whose time step control utilizes the post-processed solution. The algorithm is applied to convection-dominated convection-diffusion equations. It is shown that the length of the time step properly reflects the dynamics of the solution. The numerical costs of the adaptive algorithm are discussed
Adaptive time step control for higher order variational time discretizations applied to convection-diffusion equations
Higher order variational time stepping schemes allow an efficient
post-processing for computing a higher order solution. This paper presents an
adaptive algorithm whose time step control utilizes the post-processed
solution. The algorithm is applied to convection-dominated
convection-diffusion equations. It is shown that the length of the time step
properly reflects the dynamics of the solution. The numerical costs of the
adaptive algorithm are discussed
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