Solvability and approximation of two-side conservative fractional diffusion problems with variable-Coefficient based on least-Squares
| Autor: | Huanzhen Chen, Suxiang Yang, Vincent J. Ervin, Hong Wang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Laplace's equation
0209 industrial biotechnology Computer simulation Applied Mathematics Operator (physics) Mathematical analysis 020206 networking & telecommunications 02 engineering and technology Space (mathematics) Least squares Finite element method Computational Mathematics 020901 industrial engineering & automation 0202 electrical engineering electronic engineering information engineering Regular space Mathematics Variable (mathematics) |
| Zdroj: | Applied Mathematics and Computation. 406:126229 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2021.126229 |
| Popis: | We investigate solvability theory and numerical simulation for two-side conservative fractional diffusion equations (CFDE) with a variable-coefficient a ( x ) . We introduce σ = − a D p as an intermediate variable to isolate a ( x ) from the nonlocal operator, and then apply the least-squares method to obtain a mixed-type variational formulation. Correspondingly, solution space is split into a regular space and a kernel-dependent space. The solution p and σ are then represented as a sum of a regular part and a kernel-dependent singular part. Doing so, a new regularity theory is established, which extends those regularity results for the one side CFDE in [23, 36], and for the fractional Laplace equation corresponding to θ = 1 / 2 in [37, 38], to general CFDE with variable diffusive coefficients and for 0 θ 1 . Then, we design a kernel-independent least-squares mixed finite element approximation scheme (LSMFE). Theoretical analysis and numerical simulation demonstrate that the LSMFE can capture the singular part of the solution, approximate the solution with optimal-order accuracy, and can be easily implemented. |
| Databáze: | OpenAIRE |
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