Abstract
We prove well-posedness and regularity of solutions to a fractional diffusion porous media equation with a variable fractional order that may depend on the unknown solution. We present a linearly implicit time-stepping method to linearize and discretize the equation in time, and present rigorous analysis for the convergence of numerical solutions based on proved regularity results.
| Original language | English |
|---|---|
| Pages (from-to) | 171-207 |
| Number of pages | 37 |
| Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
| Volume | 55 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2021 |
Keywords
- Convergence
- Convolution quadrature
- Fractional diffusion equation
- Nonlinear
- Numerical approximation
- Regularity
- Variable order
- Well-posedness
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Modelling and Simulation
- Computational Mathematics
- Applied Mathematics
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