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We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\sc S. Chu, A. Kurganov, and I. Menshov}, Appl. Numer. Math.,…
Port-Hamiltonian systems provide a highly-structured framework for modeling of physical systems. By definition, they encode a balance equation relating energy changes to supplied and dissipated energy. Capturing this energy balance in…
In this paper, a self-adaptive contractive (SAC) algorithm is proposed for enhanced dynamic phasor estimation in the diverse operating conditions of modern power systems. At a high-level, the method is composed of three stages: parameter…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $d\geq 1$ dimensions. Our main approach consists of…
In this paper, we propose an adaptive finite difference scheme in order to numerically solve total variation type problems for image processing tasks. The automatic generation of the grid relies on indicators derived from a local estimation…
One difficulty in developing numerical methods for hyperbolic systems of conservation laws is the fact that solutions often contain regions where much higher resolution is required than elsewhere in the domain, particularly since the…
Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…
This paper presents new dynamic topology adaptation strategies for distributed estimation in smart grids systems. We propose a dynamic exhaustive search--based topology adaptation algorithm and a dynamic sparsity--inspired topology…
We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
This paper presents an arbitrary h.o. accurate ADER DG method on space-time adaptive meshes (AMR) for the solution of two important families of non-linear time dependent PDE for compr. dissipative flows: the compr. Navier-Stokes equations…
In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive…
In the context of the cell centered finite volume approach, care must be taken when performing the reconstruction of property gradients at cell interfaces. The present work analyzes three different gradient reconstruction procedures, using…
High order finite volume schemes for conservation laws are very useful in applications, due to their ability to compute accurate solutions on quite coarse meshes and with very few restrictions on the kind of cells employed in the…
A posteriori upper and lower bounds are derived for the linear finite element method (FEM) for the Helmholtz equation with large wave number. It is proved rigorously that the standard residual type error estimator seriously underestimates…
The simulation of hypersonic flows is computationally demanding due to large gradients of the flow variables caused by strong shock waves and thick boundary or shear layers. The resolution of those gradients imposes the use of extremely…
This paper presents a novel centralized, variational data assimilation approach for calibrating transient dynamic models in electrical power systems, focusing on load model parameters. With the increasing importance of inverter-based…