相关论文: On Symplectic, Multisymplectic Structures-Preservi…

The usual explicit finite-difference method of solving partial differential equations is limited in stability because it approximates the exact amplification factor by power-series. By adapting the same exponential-splitting method of…

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…

We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…

We give a detailed study of the symplectic geometry of a family of integrable systems obtained by coupling two angular momenta in a non trivial way. These systems depend on a parameter t $\in$ [0, 1] and exhibit different behaviors…

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n…

The main purpose of the present paper is to study from a numerical analysis point of view some robust methods designed to cope with stiff (highly anisotropic) elliptic problems. The so-called asymptotic-preserving schemes studied in this…

Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…

Finite element simulations have been used to solve various partial differential equations (PDEs) that model physical, chemical, and biological phenomena. The resulting discretized solutions to PDEs often do not satisfy requisite physical…

Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…

We present a weak finite element method for elliptic problems in one space dimension. Our analysis shows that this method has more advantages than the known weak Galerkin method proposed for multi-dimensional problems, for example, it has…

As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry. After surveying some of the most important ways of measuring the size of a symplectic set, these…

Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…

We establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions. We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms…

This short communication discusses two alternate techniques to treat hanging nodes in a quadtree mesh. Both the techniques share similarities, in that, they require only boundary information. Moreover, they do not require an explicit form…

The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…

We prove that an integrable system over a symplectic manifold, whose symplectic form is covariantly constant w.r.t. the Gauss-Manin connection, carries a natural hyper-symplectic structure. Moreover, a special Kaehler structure is induced…

We study monotone P1 finite element methods on unstructured meshes for fully non-linear, degenerately parabolic Isaacs equations with isotropic diffusions arising from stochastic game theory and optimal control and show uniform convergence…

In this manuscript we present a novel and efficient numerical method for the compressible viscous and resistive MHD equations for all Mach number regimes. The time-integration strategy is a semi-implicit splitting, combined with a hybrid…

We consider various trace formulas for the cubic Schrodinger equation in the space of infinitely smooth functions subject to periodic boundary conditions. The formulas relate conventional integrals of motion to the periods of some Abelian…

Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…