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

Author

Listed:
  • Almeida, Rui M.P.
  • Antontsev, Stanislav N.
  • Duque, José C.M.

Abstract

In this work, we study the convergence of the finite element method when applied to the following parabolic equation: ut=div(|u|γ(x,t)∇u)−λ|u|σ(x,t)−2u+f,x∈Ω⊂Rd,t∈]0,T]. 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.

Suggested Citation

  • Almeida, Rui M.P. & Antontsev, Stanislav N. & Duque, José C.M., 2017. "Discrete solutions for the porous medium equation with absorption and variable exponents," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 137(C), pages 109-129.
    • Handle: RePEc:eee:matcom:v:137:y:2017:i:c:p:109-129
    DOI: 10.1016/j.matcom.2016.12.008
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