DPG Method with Optimal Test Functions for a Fractional Advection Diffusion Equation

被引：11

作者：

Ervin, Vincent J. ^{[1
]}

Fuhrer, Thomas ^{[2
]}

Heuer, Norbert ^{[2
]}

Karkulik, Michael ^{[3
]}

机构：

[1] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA

[2] Pontificia Univ Catolica Chile, Fac Matemat, Ave Vicuna Mackenna 4860, Santiago, Chile

[3] Univ Tecn Federico Santa Maria, Dept Matemat, Ave Espana 1680, Valparaiso, Chile

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2017年 / 72卷 / 02期

关键词：

Fractional diffusion; Riemann-Liouville fractional integral; DPG method with optimal test functions; Ultra-weak formulation; FINITE-ELEMENT-METHOD; PETROV-GALERKIN DISCRETIZATION; WEAK VARIATIONAL FORMULATION; BOUNDARY-VALUE PROBLEM; DIFFERENCE METHOD; APPROXIMATIONS; SPACE; NORMS; PDES;

D O I：

10.1007/s10915-017-0369-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we define a DPG approximation with optimal test functions and show its quasi-optimal convergence. Numerical experiments confirm expected convergence properties, for uniform and adaptively refined meshes.

引用

页码：568 / 585

页数：18

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