Related papers: A spatially adaptive high-order meshless method fo…
3D Gaussian Splatting has recently achieved notable success in novel view synthesis for dynamic scenes and geometry reconstruction in static scenes. Building on these advancements, early methods have been developed for dynamic surface…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
We derive a compatible discretization method that relies heavily on the underlying geometric structure, and obeys the topological sequences and commuting properties that are constructed. As a sample problem we consider the…
A discretization method with non-matching grids is proposed for the coupled Stokes-Darcy problem that uses a mortar variable at the interface to couple the marker and cell (MAC) method in the Stokes domain with the Raviart-Thomas mixed…
A unified fluid-structure interaction (FSI) formulation is presented for solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the generalized-alpha scheme are used for the spatial and temporal discretization. The membrane…
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…
In this paper, we develop an adaptive high-order surface finite element method (FEM) incorporating the spectral deferred correction method for chain contour discretization to solve polymeric self-consistent field equations on general curved…
In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the…
We present an adaptive simulation framework for binary-fluid flows, based on the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical…
The method of regularized stokeslets is extensively used in biological fluid dynamics due to its conceptual simplicity and meshlessness. This simplicity carries a degree of cost in computational expense and accuracy because the number of…
This work introduces and assesses the efficiency of a monolithic $ph$MG multigrid framework designed for high-order discretizations of stationary Stokes systems using Taylor-Hood and Scott-Vogelius elements. The proposed approach integrates…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
In this work we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly…
The mathematical formulation, basic concept and numerical implementation of a new meshless method for solving three dimensional fluid flow and related heat transfer problems are presented in this paper. Moving least squares approximation is…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restriction of standard space-time finite element spaces on a…
The numerical analysis of higher-order mixed finite-element discretizations for saddle-point problems, such as the Stokes equations, has been well-studied in recent years. While the theory and practice of such discretizations is now…
In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall often needs to be locally refined in the region approached…