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Upper and lower solutions method for fuzzy differential equations
Springer Science and Business Media LLC - - 2010
Galerkin mixed finite element method for parabolic p-biharmonic equation with memory term
Springer Science and Business Media LLC - - Trang 1-15 - 2023
A high-order parabolic p-biLaplace equation with memory term is studied. Using Roth’s method, we managed to find the approximate solution of the time semi-discretized problem. Some a priori estimates are proved, from which we extract convergence, existence, uniqueness and qualitative results in suitable functional spaces. A full discretization scheme using the mixed finite element method is introd......
Adaptive nonconforming finite elements for the Stokes equations
Springer Science and Business Media LLC - Tập 50 - Trang 99-113 - 2013
We discuss some recent progress in the convergence analysis of adaptive finite element methods for the Stokes equations. First we present a result concerning the quasi-optimality of low-order non-conforming methods. Both the case of the Crouzeix-Raviart element on triangular meshes, and the Rannacher-Turek element on parallelogram elements are covered. Numerical experiments are conducted in order ......
New stability result for a thermoelastic Bresse system with two infinite memories
Springer Science and Business Media LLC - Tập 80 - Trang 175-200 - 2022
In this paper we investigate a thermoelastic system where the oscillations are defined by the Bresse model and the heat conduction is given by Green and Naghdi theories. First, we show that the system is well-posed in the sens of semigroup. Then, based on the energy method we establish a general decay result for the solutions of the system. This result generalizes and improves the earlier work of ......
A highly accurate scheme for solving the thin plate equation
Springer Science and Business Media LLC - - Trang 1-15 - 2023
This paper reports a new bi-quintic B-spline collocation method for numerically solving bi-harmonic problems with Dirichlet boundary conditions on the rectangular domain. Solving these problems with standard bi-quintic B-spline collocation provides only second-order convergence. To overcome this limitation, we formulate a sixth-order collocation scheme, namely, the one-step left and right-hand sid......
On the weak consistency of finite volumes schemes for conservation laws on general meshes
Springer Science and Business Media LLC - Tập 76 - Trang 581-594 - 2019
The aim of this paper is to develop some tools in order to obtain the weak consistency of (in other words, an analogue of the Lax–Wendroff theorem for) finite volume schemes for balance laws in the multi-dimensional case and under minimal regularity assumptions for the mesh. As in the seminal Lax–Wendroff paper, our approach relies on a discrete integration by parts of the weak formulation of the ......
The radiative transfer model for the greenhouse effectAbstract Radiative transfer is at the heart of the mechanism to explain the greenhouse effect based on the partial infrared opacity of carbon dioxide, methane and other greenhouse gases in the atmosphere. In absence of thermal diffusion, the mathematical model consists of a first order integro-differential equation coupled with an integral equation for the light int... ...
Springer Science and Business Media LLC - Tập 79 Số 3 - Trang 489-525 - 2022
A priori error analysis of the fully discretized time-dependent coupled Darcy and Stokes equations
Springer Science and Business Media LLC - Tập 73 - Trang 97-119 - 2016
In this paper, we study the time-dependent Darcy and Stokes equations, that model laminar fluid flow over a porous medium, in two- or three-dimensional connected open domains which are coupled via appropriate matching conditions on the interface. The problem is discretized by the backward Euler scheme in time and finite elements in space. We prove a priori error estimates as a function of the time......
Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review
Springer Science and Business Media LLC - - 2024
Hyperbolic systems with stiff relaxation constitute a wide class of evolutionary partial differential equations which describe several physical phenomena, ranging from gas dynamics to kinetic theory, from semiconductor modeling to traffic flow. Peculiar features of such systems is the presence of a small parameter that determines the smallest time scale of the system. As such parameter vanishes, t......
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