CMA - Centro de Matemática e Aplicações da UBI
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CMA, Centre of Mathematics and Applications, is a research unit in Mathematics and Applications, hosted by University of Beira Interior (UBI). UBI provides the requested facilities, budget management, computing support and institutional framework to wards CMA’s activities.
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Browsing CMA - Centro de Matemática e Aplicações da UBI by Author "Almeida, Rui M.P."
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- Discrete solutions for the porous medium equation with absorption and variable exponentsPublication . Almeida, Rui M.P.; Antontsev, Stanislav N.; Duque, José C. M.In this work, we study the convergence of the finite element method when applied to the following parabolic equation: Since the equation may be of degenerate type, we use an approximate problem, regularized by introducing a parameter ε. We prove, under certain conditions on γ, σ and f, that the weak solution of the approximate problem converges to the weak solution of the initial problem, when the parameter ε tends to zero. The convergence of the discrete solutions for the weak solution of the approximate problem is also proved. Finally, we present some numerical results of a MatLab implementation of the method.
- Finite element schemes for a class of nonlocal parabolic systems with moving boundariesPublication . Almeida, Rui M.P.; Duque, José C. M.; Ferreira, Jorge; Robalo, RuiThe aim of this paper is to study the convergence, properties and error bounds of the discrete solutions of a class of nonlinear systems of reaction–diffusion nonlocal type with moving boundaries, using the finite element method with polynomial approximations of any degree and some classical time integrators. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with a moving finite element method are investigated.
- Moving Finite Element MethodPublication . Coimbra, M. D. C.; Rodrigues, Alirio Egidio; Rodrigues, Jaime Duarte; Robalo, Rui J.; Almeida, Rui M.P.His book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.
- On the finite element method for a nonlocal degenerate parabolic problemPublication . Almeida, Rui M.P.; Antontsev, Stanislav N.; Duque, José C. M.The aim of this paper is the numerical study of a class of nonlinear nonlocal degenerate parabolic equations. The convergence and error bounds of the solutions are proved for a linearized Crank–Nicolson–Galerkin finite element method with polynomial approximations of degree k≥1. Some explicit solutions are obtained and used to test the implementation of the method in Matlab environment.
- On the packing process in a shoe manufacturerPublication . Vieira, Manuel V. C.; Ferreira, Flora; Duque, José C. M.; Almeida, Rui M.P.This paper addresses a shoe packing problem that is motivated by an industry applicationand involves two main stages: (i) packing shoes into suitable boxes and (ii) loading thepacked shoes into three dimensional open-dimension containers. This is the first study deal-ing with the packing of small boxes into several containers where each container has allthree dimensions open. Assigning shoes to a minimum number of box types is achievedusing a 0–1 program, whereas the loading problem is tackled via a mixed-integer nonlinearprogram that minimizes the total volume of the container. That latter model is linearized byusing a simple summation of the container dimensions, which is compared against a moreelaborated linearization scheme. The effectiveness and efficiency of the proposed schemeare demonstrated with numerical experiments using real-world instances.
- A reaction-diffusion model for a class of nonlinear parabolic equations with moving boundaries: Existence, uniqueness, exponential decay and simulationPublication . Robalo, Rui J.; Almeida, Rui M.P.; Coimbra, M. D. C.; Ferreira, JorgeThe aim of this paper is to establish the existence, uniqueness and asymptotic behaviour of a strong regular solution for a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries:where is a bounded non-cylindrical domain defined byMoreover, we study the properties of the solution and implement a numerical algorithm based on the Moving Finite Element Method (MFEM) with polynomial approximations of any degree, to solve this class of problems. Some numerical tests are investigated to evaluate the performance of our Matlab code based on the MFEM and illustrate the exponential decay of the solution.
- The Crank–Nicolson–Galerkin Finite Element Method for a Nonlocal Parabolic Equation with Moving BoundariesPublication . Almeida, Rui M.P.; Duque, José C. M.; Ferreira, Jorge; Robalo, Rui J.The aim of this article is to establish the convergence and error bounds for the fully discrete solutions of a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries, using a linearized Crank–Nicolson–Galerkin finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with some existing moving finite element methods are investigated.