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Second-Order Semi-Lagrangian Exponential Time Differencing Method with Enhanced Error Estimate for the Convective Allen–Cahn Equation
The convective Allen–Cahn (CAC) equation has been widely used for simulating multiphase flows of incompressible fluids, which contains an extra...
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Semi-Lagrangian finite element exterior calculus for incompressible flows
We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions on arbitrary...
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Fourth-Order Conservative Non-splitting Semi-Lagrangian Hermite WENO Schemes for Kinetic and Fluid Simulations
We present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport...
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Meshfree Semi-Lagrangian Methods for Solving Surface Advection PDEs
We analyze a class of meshfree semi-Lagrangian methods for solving advection problems on smooth, closed surfaces with solenoidal velocity field. In...
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A High-Order Semi-Lagrangian Finite Difference Method for Nonlinear Vlasov and BGK Models
In this paper, we propose a new conservative high-order semi-Lagrangian finite difference (SLFD) method to solve linear advection equation and the...
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A semi-Lagrangian scheme for Hamilton–Jacobi–Bellman equations with oblique derivatives boundary conditions
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton–Jacobi–Bellman (HJB)...
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On the Construction of Conservative Semi-Lagrangian IMEX Advection Schemes for Multiscale Time Dependent PDEs
This article is devoted to the construction of a new class of semi-Lagrangian (SL) schemes with implicit-explicit (IMEX) Runge-Kutta (RK) time...
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A Class of Positive Semi-discrete Lagrangian–Eulerian Schemes for Multidimensional Systems of Hyperbolic Conservation Laws
In this paper, we design and analyze a new class of positive Semi-Discrete Lagrangian–Eulerian (SDLE) schemes for solving multidimensional initial...
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A Conservative Semi-Lagrangian Finite Volume Method for Convection–Diffusion Problems on Unstructured Grids
A conservative semi-Lagrangian finite volume method is presented for the numerical solution of convection–diffusion problems on unstructured grids....
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Second Order Fully Semi-Lagrangian Discretizations of Advection-Diffusion-Reaction Systems
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which is...
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Semi-Lagrangian Subgrid Reconstruction for Advection-Dominant Multiscale Problems with Rough Data
We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical...
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High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation
In this paper, we present a semi-Lagrangian (SL) method based on a non-polynomial function space for solving the Vlasov equation. We find that a...
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A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes
In this paper, we present a conservative semi-Lagrangian scheme designed for the numerical solution of 3D hydrostatic free surface flows involving...
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A Corrected Inexact Proximal Augmented Lagrangian Method with a Relative Error Criterion for a Class of Group-Quadratic Regularized Optimal Transport Problems
The optimal transport (OT) problem and its related problems have attracted significant attention and have been extensively studied in various...
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Local convergence analysis of augmented Lagrangian method for nonlinear semidefinite programming
The augmented Lagrangian method (ALM) has gained tremendous popularity for its elegant theory and impressive numerical performance since it was...
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Bernstein-Bézier Galerkin-Characteristics Finite Element Method for Convection-Diffusion Problems
A class of Bernstein-Bézier basis based high-order finite element methods is developed for the Galerkin-characteristics solution of...
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Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for...
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An instantaneous semi-Lagrangian approach for boundary control of a melting problem
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth...
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A Semi-Implicit Numerical Method for Differentially Rotating Compressible Flows
AbstractIn astrophysical fluid dynamics, some types of flows, like e.g., magnetorotational supernova explosions, deal with a highly variable Mach...
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A Conservative Eulerian–Lagrangian Runge–Kutta Discontinuous Galerkin Method for Linear Hyperbolic System with Large Time Step**
We propose an Eulerian–Lagrangian (EL) Runge–Kutta (RK) discontinuous Galerkin (DG) method for a linear hyperbolic system. The method is designed...
