Tuesday, February 15, 2022 - 14:15 in V5-148 + Zoom
Structural stability and convergence of fully practical Finite Volume discretizations for p(x) and p(u)-laplacian elliptic problems
A talk in the BI.discrete series by
Boris Andreianov from Université de Tours, France
| Abstract: |
We will expose a practical approach of passage to the limit in approximations of variable-exponent elliptic problems is absence of a fixed functional framework of $W^{1,p(.)}$ kind. Based on the Young measure technique (mainly following the approach of Doltzmann, Hüngerbuhler, Müller) and on the technical notion of renormalized solutions to elliptic PDEs with merely $L^1$ source term, we establish stability for broad and narrow solutions (aka W-solutions and H-solutions) under the adequate assumptions on the convergence of the associated sequence of variable exponents $(p_n(.))_n$.
We then apply the convergence analysis technique to Finite Volume approximations by different discretization methods enjoying the Discrete Duality feature. In addition to the main convergence result for the log-Hölder exponent case, we discuss the behaviour of different schemes in the setting of the Zhikov counterexample featuring the Lavrentiev gap for the associated optimization problems.
The techniques allow to deal with local and non-local $u$-dependence of the variable exponent $p(.)$.
Joint work with M. Bendahmane and S. Ouaro (Nonlin. Analysis, 2010) and ongoing work with E.H. Quenjel.
Within the CRC this talk is associated to the project(s): A7 |
Back
