Li, Yuan Zhai, Chunfang
Published in
Advances in Computational Mathematics

In this paper, a second-order backward differentiation formula (BDF) scheme for a hybrid MHD system is considered. Being different with the steady and nonstationary MHD equations, the hybrid MHD system is coupled by the time-dependent Navier-Stokes equations and the steady Maxwell equations. By using the standard extrapolation technique for the non...

Adak, D. Natarajan, S.
Published in
Advances in Computational Mathematics

In this paper, we consider the discretization of a parabolic nonlocal problem within the framework of the virtual element method. Using the fixed point argument, we prove that the fully discrete scheme has a unique solution. The presence of the nonlocal term makes the problem nonlinear, and the resulting nonlinear equations are solved using the New...

de Carvalho, Pitágoras Pinheiro Fernández-Cara, Enrique Ferrel, Juan Bautista Límaco
Published in
Advances in Computational Mathematics

This paper deals with the numerical implementation of a systematic method for solving bi-objective optimal control problems for wave equations. More precisely, we look for Nash and Pareto equilibria which respectively correspond to appropriate noncooperative and cooperative strategies in multi-objective optimal control. The numerical methods descri...

Lu, Jian Jiang, Qingtang Li, Lin
Published in
Advances in Computational Mathematics

The synchrosqueezing transform (SST) was developed recently to separate the components of non-stationary multicomponent signals. The continuous wavelet transform-based SST (WSST) reassigns the scale variable of the continuous wavelet transform of a signal to the frequency variable and sharpens the time-frequency representation. The WSST with a time...

Zhou, Yanhui Wu, Jiming
Published in
Advances in Computational Mathematics

This paper presents a general framework for the coercivity analysis of a class of quadratic finite volume element (FVE) schemes on triangular meshes for solving elliptic boundary value problems. This class of schemes covers all the existing quadratic schemes of Lagrange type. With the help of a new mapping from the trial function space to the test ...

Floater, Michael S. Hu, Kaibo
Published in
Advances in Computational Mathematics

We consider spline functions over simplicial meshes in ℝn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {R}^{n}$\end{document}. We assume that the spline pieces...

Fryklund, Fredrik Kropinski, Mary Catherine A. Tornberg, Anna-Karin
Published in
Advances in Computational Mathematics

Integral equation–based numerical methods are directly applicable to homogeneous elliptic PDEs and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, such a method is extended to the heat equation with inhomogeneous source terms. First, the heat equation is discretised in time, then in each time step we...

Meng, Jian Mei, Liquan
Published in
Advances in Computational Mathematics

In this paper, we give a presentation of virtual element method for the approximation of the vibration problem of clamped Kirchhoff plate, which involves the biharmonic eigenvalue problem. Following the theory of Babǔska and Osborn, the error estimates of the discrete scheme for the degree k ≥ 2 of polynomials are standard results. However, when c...

Epshteyn, Yekaterina Xia, Qing
Published in
Advances in Computational Mathematics

In this work, we consider parabolic models with dynamic boundary conditions and parabolic bulk-surface problems in 3D. Such partial differential equations–based models describe phenomena that happen both on the surface and in the bulk/domain. These problems may appear in many applications, ranging from cell dynamics in biology, to grain growth mode...

Gu, Zhendong
Published in
Advances in Computational Mathematics

A spectral collocation method is developed to solve a nonlinear Caputo fractional differential system. The main idea is to solve the corresponding system of weakly singular nonlinear Volterra integral equations (VIEs). The convergence analysis in matrix form shows that the presented method has spectral convergence. Numerical experiments are carried...