Related papers: SM stability for time-dependent problems
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
We explore in this article the possibilities and limitations of the so-called energy method for analyzing the stability of finite difference approximations to the transport equation with extrapolation numerical boundary conditions at the…
Finite difference schemes for the simulation of elastic waves in materi- als with jump discontinuities are presented. The key feature is the highly accurate treatment of interfaces where media discontinuities arise. The schemes are…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
A unified approach to derive optimal finite differences is presented which combines three critical elements for numerical performance especially for multi-scale physical problems, namely, order of accuracy, spectral resolution and…
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing schemes for the equation with variable coefficients have…
In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…
The goal of this work is to determine classes of traveling Solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz.
This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…
We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with…
The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
Two-fluid ideal plasma equations are a generalized form of the ideal MHD equations in which electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account…
This paper addresses the question whether there are numerical schemes for constant-coefficient advection problems that can yield convergent solutions for an infinite time horizon. The motivation is that such methods may serve as building…
Parameterized Sequential Decision Making (Para-SDM) framework models a wide array of network design applications spanning supply-chain, transportation, and sensor networks. These problems entail sequential multi-stage optimization…
We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution…