Related papers: Petrov-Galerkin and Spectral Collocation Methods f…
This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…
In collisionless and weakly collisional plasmas, the particle distribution function is a rich tapestry of the underlying physics. However, actually leveraging the particle distribution function to understand the dynamics of a weakly…
This paper proposes and analyzes an implicit-explicit BDF-Galerkin scheme of second order for the time-dependent nonlinear thermistor problem. For this, we combine the second-order backward differentiation formula with special extrapolation…
In this work we explore the Sibuya discrete probability distribution, which serves as the basis and the main instrument for numerical simulations of Grunwald--Letnikov fractional derivatives by the Monte Carlo method. We provide three…
In this paper, we discuss the different splitting approaches to solve the Gross-Pitaevskii equation numerically. We consider conservative finite-difference schemes and spectral methods for the spatial discretisation. Further, we apply…
Continuous Galerkin Petrov time discretization scheme is tested on some Hamiltonian systems including simple harmonic oscillator, Kepler's problem with different eccentricities and molecular dynamics problem. In particular, we implement the…
We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (APG) method, is derived by decomposing the generalized…
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…
We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator, we explore the performance of algorithms for computing its…
We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
A novel domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations…
We study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data. With the stochastic Galerkin approach, the solutions are represented as…
We propose a novel and simple spectral method based on the semi-discrete Fourier transforms to discretize the fractional Laplacian $(-\Delta)^\frac{\alpha}{2}$. Numerical analysis and experiments are provided to study its performance. Our…
This paper develops a discontinuous Galerkin (DG) finite element differential calculus theory for approximating weak derivatives of Sobolev functions and piecewise Sobolev functions. By introducing numerical one-sided derivatives as…
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as "FEAST", has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute…
We consider a fully discretized numerical scheme for parabolic stochastic partial differential equations with multiplicative noise. Our abstract framework can be applied to formulate a non-iterative domain decomposition approach. Such…
In this article, several discontinuous Petrov-Galerkin (DPG) methods with perfectly matched layers (PMLs) are derived along with their quasi-optimal graph test norms. Ultimately, two different complex coordinate stretching strategies are…
Petrov-Galerkin methods are always considered in numerical solutions of differential and integral equations $ Ax=b $. It is common to consider the convergence and error analysis when $ b \in \mathcal{R}(A) $ which make the equation…
The optimal Petrov-Galerkin formulation to solve partial differential equations (PDEs) recovers the best approximation in a specified finite-dimensional (trial) space with respect to a suitable norm. However, the recovery of this optimal…