Related papers: Collocation Methods for High-Order Well-Balanced M…
Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic…
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…
In this work, we develop a high-order pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
Imbalanced problems can arise in different real-world situations, and to address this, certain strategies in the form of resampling or balancing algorithms are proposed. This issue has largely been studied in the context of classification,…
We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…
High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
Balanced truncation, a technique from robust control theory, is a systematic method for producing simple approximate models of complex linear systems. This technique may have significant applications in physics, particularly in the study of…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order…
We propose a general framework of iteratively reweighted l1 methods for solving lp regularization problems. We prove that after some iteration k, the iterates generated by the proposed methods have the same support and sign as the limit…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
In this work, the high order accuracy and the well-balanced (WB) properties of some novel continuous interior penalty (CIP) stabilizations for the Shallow Water (SW) equations are investigated. The underlying arbitrary high order numerical…
We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…
To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
The paper is devoted to well-posedness analysis and the numerical solution of a family of general elliptic mixed variational-hemivariational inequalities. Various mixed variational equations, mixed variational inequalities and mixed…