Discrete solutions for the porous medium equation with absorption and variable exponents

• Autor(a) principal: Almeida, Rui M.P.
• Data de Publicação: 2017
• Outros Autores: Antontsev, Stanislav N., Duque, José C. M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.6/9089
• topic: Porous medium equation; Finite element method; Variable exponents

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.