We derive and analyze a fully computable discrete scheme for fractional partial differential equations posed on the full space $\mathbb{R}^d$ . Based on a reformulation using the well-known Caffarelli-Silvestre extension, we study a modified variational formulation to obtain well-posedness of the discrete problem. Our scheme is obtained by combining a diagonalization procedure with a reformulation using boundary integral equations and a coupling of finite elements and boundary elements. For our discrete method we present a-priori estimates as well as numerical examples.

翻译：我们根据使用著名的Caffarelli-Silvestre扩展的重新版图,研究一种修改的变异配方,以获得离散问题的充分位置。我们的方法是通过将分解程序与使用边界整体方程的重新版图和有限元素和边界元素的组合结合起来,获得的。对于我们的离散方法,我们提出了优先估计以及数字实例。