Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions

Fractal and Fractional

Gábor Maros¹  Ferenc Izsák¹ 

[1] Department of Applied Analysis and Computational Mathematics & NumNet MTA-ELTE Research Group, Eötvös Loránd University, Pázmány P. stny. 1C, 1117 Budapest, Hungary;

关键词: fractional Laplacian;    elliptic boundary value problems;    boundary integral equations;    boundary element methods;    Riesz potential;   

DOI  :  10.3390/fractalfract5030075

来源: DOAJ

【 摘 要 】

The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian operator. The basis of the convergence analysis for a lower-order boundary element approximation is the theory for the corresponding continuous problem. In particular, we need continuity results for Riesz potentials and the fractional-order extension of the theory for boundary integral equations with the Laplacian operator. Accordingly, the convergence is stated in fractional-order Sobolev norms. The results were confirmed in a numerical experiment.

【 授权许可】

Unknown