相关论文: Geometric-algebraic approach to acid-base equilibr…

This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually…

A new weak Galerkin (WG) finite element method for solving the biharmonic equation in two or three dimensional spaces by using polynomials of reduced order is introduced and analyzed. The WG method is on the use of weak functions and their…

We study the closure of approximating sequences of some diffusion equations under certain weak convergence. A specific description of the closure under weak $H^1$-convergence is given, which reduces to the original equation when the…

We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a…

Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…

This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…

The intuitive sphere-packing argument is used to obtain analytically-tractable closed-form approximations for achievable information rates of coded modulation transmission systems, for which only analytically-intractable expressions are…

equilibrium-c (eqc) is a program for computing the composition of gas mixtures in chemical equilibrium. In typical usage, the program is given a known thermodynamic state, such as fixed temperature and pressure, as well as an initial…

A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…

In this paper we consider the one dimensional quantum hydrodynamics (QHD) system, with a genuine hydrodynamic approach. The global existence of weak solutions with large data has been obtained in [2, 3], in several space dimensions, by…

In this work we study a DPG method for an ultra-weak variational formulation of a reaction-diffusion problem. We improve existing a priori convergence results by sharpening an approximation result for the numerical flux. By duality…

In this research note we provide a variational basis for the optimal artificial diffusion method, which has been a cornerstone in developing many stabilized methods. The optimal artificial diffusion method produces exact nodal solutions…

We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…

The EHP and the MCAP provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. Both approaches utilize the mixed formulation and lead to the development of…

We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive…

We propose a system-oriented basis-set design based on even-tempered basis functions to variationally encode electronic ground-state information into molecular orbitals. First, we introduce a reduced formalism of concentric even-tempered…

A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results…

We present recent computer algebra methods that support the calculations of (multivariate) series solutions for (certain coupled systems of partial) linear differential equations. The summand of the series solutions may be built by…

In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…