相关论文: On Symplectic, Multisymplectic Structures-Preservi…
A new numerical method is presented for solving the rotating shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical…
We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to…
We study the Euler-Lagrange cohomology and explore the symplectic or multisymplectic geometry and their preserving properties in classical mechanism and classical field theory in Lagrangian and Hamiltonian formalism in each case…
In simulation sciences, it is desirable to capture the real-world problem features as accurately as possible. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the…
This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.
We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the perturbative context to suitably modify the classical Finite…
We show that, when applied to any non-canonical Hamiltonian system, any integrator that is symplectic for canonical Hamiltonian problems is actually conjugate symplectic for the non-canonical structure. This result is useful because it…
This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite…
We consider a parameter dependent family of damped hyperbolic equations with interesting limit behavior: the system approaches steady states exponentially fast and for parameter to zero the solutions converge to that of a parabolic limit…
Evolutionary partial differential equations play a crucial role in many areas of science and engineering. Spatial discretization of these equations leads to a system of ordinary differential equations which can then be solved by numerical…
In this short note, we present a multi-symplectic structure of the Serre-Green-Naghdi (SGN) equations modelling nonlinear long surface waves in shallow water. This multi-symplectic structure allow the use of efficient finite difference or…
In this paper, we consider a nonlinear and nonlocal parabolic model for multi-species ionic fluids and introduce a semi-implicit finite volume scheme, which is second order accurate in space, first order in time and satisfies the following…
In this paper, we prove necessary and sufficient conditions for a hybridizable discontinuous Galerkin (HDG) method to satisfy a multisymplectic conservation law, when applied to a canonical Hamiltonian system of partial differential…
A numerical procedure providing guaranteed two-sided bounds on the effective coefficients of elliptic partial differential operators is presented. The upper bounds are obtained in a standard manner through the variational formulation of the…
In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…
This work is devoted to design and study efficient and accurate numerical schemes to approximate a chemo-attraction model with consumption effects, which is a nonlinear parabolic system for two variables; the cell density and the…
We have researched the condition for symplectic discretization to preserve local boundedness for the space of 2-dimensional Hamiltonian dynamical systems in this paper.