2,047 research outputs found
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
An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations
In this article we propose a new symmetric version of the
interior penalty discontinuous Galerkin finite element
method for the numerical approximation
of the compressible Navier-Stokes equations. Here, particular
emphasis is devoted to the construction of an optimal numerical
method for the evaluation of certain target functionals of practical
interest, such as the lift and drag coefficients of a body immersed in a
viscous fluid. With this in mind, the key ingredients in the
construction of the method include: (i) An adjoint consistent imposition of
the boundary conditions; (ii) An adjoint consistent reformulation of the
underlying target functional of practical interest; (iii) Design of appropriate
interior--penalty stabilization terms. Numerical experiments presented
within this article clearly indicate the optimality of the proposed
method when the error is measured in terms of both the L2-norm, as well as
for certain target functionals. Computational comparisons with
other discontinuous Galerkin schemes proposed in the literature,
including the second scheme
of Bassi and Rebay, the standard SIPG method
outlined in [Hartmann,Houston-2006], and an NIPG variant of the new scheme
will be undertaken
Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows
In this article we develop both the a priori and a posteriori error analysis of hp–version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain = 2,3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp–adaptive refinement algorithm
Adaptive discontinuous Galerkin approximations to fourth order parabolic problems
An adaptive algorithm, based on residual type a posteriori indicators of
errors measured in and norms, for a numerical
scheme consisting of implicit Euler method in time and discontinuous Galerkin
method in space for linear parabolic fourth order problems is presented. The a
posteriori analysis is performed for convex domains in two and three space
dimensions for local spatial polynomial degrees . The a posteriori
estimates are then used within an adaptive algorithm, highlighting their
relevance in practical computations, which results into substantial reduction
of computational effort
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