Motivated by the pricing of American options for baskets we consider a parabolic variational inequality in a bounded polyhedral domain Ω ⊂ R with a continuous piecewise smooth obstacle. We formulate a fully discrete method by using piecewise linear finite elements in space and the backward Euler method in time. We define an a posteriori error estimator and show that it gives an upper bound for ...

We present a new approach for predicting spatial phase signals originated from photothermally excited metallic nanoparticles of arbitrary shapes and sizes. Heat emitted from the nanoparticle affects the measured phase signal via both the nanoparticle surrounding refractive index and thickness changes. Since these particles can be bio-functionalized to bind certain biological cell components, th...

Numerical methods for design sensitivity analysis of multibody dynamics are presented. An analysis of the index-3 adjoint differential-algebraic equations is conducted and stability of the integration of the adjoint differential-algebraic equations in the backward direction is proven. Stabilized index-1 formulations are presented and convergence of backward differentiation formulas is shown for...

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear bou...

The paper is devoted to the numerical solution of an elastoplastic constitutive initial value problem containing the Mohr-Coulomb yield criterion, a nonassociative plastic flow rule, and a nonlinear isotropic hardening. The constitutive problem is discretized by the implicit Euler method. Instead of the conventional Koiter formulations, we define the plastic flow rule using the subdifferential ...

We introduce two biparametric families of Apostol-Frobenius-Euler polynomials level-$m$. give some algebraic properties, as well other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers second kind, Apostol--Bernoulli polynomials, Apostol--Genocchi Apostol--Euler and Jacobi polynomials. Finally, we will show differential properties this new family

One of the new research fields in plasticity is related to choosing a proper non-associated flow rule (NAFR), instead of the associated one (AFR), to predict the experimental results more accurately. The idea of the current research is derived from combining von Mises and Tresca criteria in the places of yield and plastic potential surfaces in rate-independent plasticity.  This idea is implemen...

This paper presents a sliding mode filter for removing noise. It effectively removes impulsive noise and high-frequency noise with producing smaller phase lag than linear filters. In addition, it is less prone to overshoot than previous sliding mode filters and it does not produce chattering. It is computationally inexpensive, and thus suitable for realtime applications. The proposed sliding mo...