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High-order methods beyond the classical complexity bounds: inexact high-order proximal-point methods
We introduce a Bi-level OPTimization (BiOPT) framework for minimizing the sum of two convex functions, where one of them is smooth enough. The BiOPT...
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Efficient Iterative Arbitrary High-Order Methods: an Adaptive Bridge Between Low and High Order
We propose a new paradigm for designing efficient p -adaptive arbitrary high-order methods. We consider arbitrary high-order iterative schemes that...
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High-order finite difference methods
Finite difference (FD) methods are very popular for solving partial differential equations (PDEs) because of their simplicity. A simple but powerful...
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High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation
We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty...
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New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with...
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Arbitrary high-order structure-preserving methods for the quantum Zakharov system
In this paper, we present a new methodology to develop arbitrary high-order structure-preserving methods for solving the quantum Zakharov system. The...
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Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1 Selected Papers from the ICOSAHOM Conference, Vienna, Austria, July 12-16, 2021
The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed...
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High Order Absolutely Convergent Fast Swee** Methods with Multi-resolution WENO Local Solvers for Eikonal and Factored Eikonal Equations
Fast swee** methods are a class of efficient iterative methods developed in the literature to solve steady-state solutions of hyperbolic partial...
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Efficient High-Order Space-Angle-Energy Polytopic Discontinuous Galerkin Finite Element Methods for Linear Boltzmann Transport
We introduce an hp -version discontinuous Galerkin finite element method (DGFEM) for the linear Boltzmann transport problem. A key feature of this new...
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High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models
In this paper, we explore bound preserving and high-order accurate local discontinuous Galerkin (LDG) schemes to solve a class of chemotaxis models,...
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High-Order Bound-Preserving Local Discontinuous Galerkin Methods for Incompressible and Immiscible Two-Phase Flows in Porous Media
In this paper, we develop high-order bound-preserving (BP) local discontinuous Galerkin methods for incompressible and immiscible two-phase flows in...
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Phase Error Analysis of Implicit Runge–Kutta Methods: New Classes of Minimal Dissipation Low Dispersion High Order Schemes
In the current research, we analyze dissipation and dispersion characteristics of the most accurate two and three-stage Gauss–Legendre implicit...
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High Order Compact Central Spatial Discretization Under the Framework of Entropy Split Methods
Yee and Sjögreen (Comput Fluid 37:593–619, 2008) did a study on the performance between high order compact (Padé) spatial central finite...
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Development of turbulent inflow methods for the high order HPC framework FLEXI
Turbulent inflow methods offer new possibilities for an efficient simulation by reducing the computational domain to the interesting parts. Typical...
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Accuracy-Enhancement of Discontinuous Galerkin Methods for PDEs Containing High Order Spatial Derivatives
In this paper, we consider the accuracy-enhancement of discontinuous Galerkin (DG) methods for solving partial differential equations (PDEs) with...
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Inexact accelerated high-order proximal-point methods
In this paper, we present a new framework of bi-level unconstrained minimization for development of accelerated methods in Convex Programming. These...
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First- and second-order high probability complexity bounds for trust-region methods with noisy oracles
In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value and...
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