Abstract Lagrangian trajectories are widely used as observations for recovering the underlying flow field via data assimilation (DA). However, strong nonlinearity in observational process and high dimensionality of problems often cause challenges applying standard DA. In this paper, a Lagrangian‐Eulerian multiscale DA (LEMDA) framework is developed. It starts with exploiting Boltzmann kinetic description particle dynamics to derive set continuum equations, which characterize statistical...

We study the approximation of spectrum a second-order elliptic differential operator by Hybrid High-Order (HHO) method. The HHO method is formulated using cell and face unknowns which are polynomials some degree $k\geq 0$. key idea for discrete eigenvalue problem to introduce where have been eliminated. Using abstract theory spectral compact operators in Hilbert spaces, we prove that eigenvalues converge as $h^{2t}$ eigenfunctions $h^{t}$ $H^1$-seminorm, $h$ mesh-size, $t\in [s,k+1]$ depends...

.Sea ice profoundly influences the polar environment and global climate. Traditionally, sea has been modeled as a continuum under Eulerian coordinates to describe its large-scale features, using, for instance, viscous-plastic rheology. Recently, Lagrangian particle models, also known discrete element method have utilized characterizing motion of individual fragments (called floes) at scales 10 km smaller, especially in marginal zones. This paper develops multiscale model that couples systems...

We use blended quadrature rules to reduce the phase error of isogeometric analysis discretizations. To explain observed behavior and quantify approximation errors, we generalized Pythagorean eigenvalue theorem account for errors on resulting weak forms [28]. The proposed techniques improve spectral accuracy uniform non-uniform meshes different polynomial orders continuity basis functions. convergence rate optimally schemes is increased by two with respect case when standard quadratures are...

Abstract We present a variationally separable splitting technique for the generalized‐ α method solving parabolic partial differential equations. develop tensor‐product mesh which results in solver with linear cost respect to total number of degrees freedom system multidimensional problems. consider finite elements and isogeometric analysis spatial discretization. The overall maintains user‐controlled high‐frequency dissipation while minimizing unwanted low‐frequency dissipation. has...

The generalized-α method encompasses a wide range of time integrators. possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation. Additionally, the numerical can be controlled by user setting single parameter, ρ∞. is unconditionally stable and has second-order accuracy in time. We extend to third-order parameter. In each step, scheme only requires inverting one matrix on acceleration update displacement velocity explicitly. establish that stable. discuss...

In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The method solves stationary advection-dominated diffusion problems.We stabilize via residual minimization. We discretize problem using B-spline basis functions. then seek to minimize isogeometric over a spline space built on tensor product mesh. construct solution smooth subspace of residual. can specify by reducing polynomial order, increasing continuity, or combination these. Gramm matrix for minimization is...

Abstract We propose a new class of high‐order time‐marching schemes with dissipation control and unconditional stability for parabolic equations. High‐order time integrators can deliver the optimal performance highly accurate robust spatial discretizations such as isogeometric analysis. The generalized‐ method delivers second‐order accuracy in controls numerical discrete spectrum's high‐frequency region. extend methodology to obtain marching methods high range. Furthermore, we maintain...

The Schrödinger equation with random potentials is a fundamental model for understanding the behavior of particles in disordered systems. Disordered media are characterised by complex that lead to localisation wavefunctions, also called Anderson localisation. These wavefunctions may have similar scales eigenenergies which poses difficulty their discovery. It has been longstanding challenge due high computational cost and complexity solving equation. Recently, machine-learning tools adopted...