Related papers: On a Nonuniform Crank-Nicolson Scheme for Solving …
We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, we derive proper a priori bounds, based on which, we prove…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
This paper introduces the basic concepts for physics-compatible discretization techniques. The paper gives a clear distinction between vectors and forms. Based on the difference between forms and pseudo-forms and the $\star$-operator which…
We present promising initial results of our adaptive multigrid solver developed for application directly to the non-Hermitian Wilson-Dirac system in 4 dimensions, as opposed to the solver developed in [1] for the corresponding normal…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
In this paper, we investigate the numerical solutions of the cubic nonlinear Schrodinger equation via the exponential B-spline collocation method. Crank-Nicolson formulas are used for time discretization of the target equation. A…
In this paper, we study the stability and convergence of a fully discrete finite difference scheme for the initial value problem associated with the Korteweg-De Vries (KdV) equation. We employ the Crank-Nicolson method for temporal…
This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the…
In this paper we present a possible model of adaptive grids for numerical resolution of differential problems, using physical or geometrical properties, as viscosity or velocity gradient of a moving fluid. The relation between the values of…
Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…
Stochastic Klein--Gordon--Schr\"odinger (KGS) equations are important mathematical models and describe the interaction between scalar nucleons and neutral scalar mesons in the stochastic environment. In this paper, we propose novel…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
This paper analyses the numerical solution of a class of non-linear Schr\"odinger equations by Galerkin finite elements in space and a mass- and energy conserving variant of the Crank-Nicolson method due to Sanz-Serna in time. The novel…
This paper investigates quenching solutions of an one-dimensional, two-sided Riemann-Liouville fractional order convection-diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in…
The main objective of this paper is to present an efficient structure-preserving scheme, which is based on the idea of the scalar auxiliary variable approach, for solving the space fractional nonlinear Schr\"{o}dinger equation. First, we…
We present a variational quantum algorithm for structural mechanical problems, specifically addressing crack opening simulations that traditionally require extensive computational resources. Our approach provides an alternative solution for…
The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easily constructed and relatively uncomplicated to investigate…
The problem of controlling and stabilising solutions to the Kuramoto-Sivashinsky equation is studied in this paper. We consider a generalised form of the equation in which the effects of an electric field and dispersion are included. Both…
We consider a model initial- and Dirichlet boundary- value problem for a fourth-order linear stochastic parabolic equation, in one space dimension, forced by an additive space-time white noise. First, we approximate its solution by the…
In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…