Numerical Solution of Parabolic Problems Based on a Weak Space-Time Formulation

作者：Larsson Stig; Molteni Matteo^*

来源：Computational Methods in Applied Mathematics, 2017, 17(1): 65-84.

DOI：10.1515/cmam-2016-0027

• Inf-Sup
• Space-Time
• Superconvergence
• Quasi-Optimality
• Finite Element
• Error Estimate
• Petrov-Galerkin

We investigate a weak space-time formulation of the heat equation and its use for the construction of a numerical scheme. The formulation is based on a known weak space-time formulation, with the difference that a pointwise component of the solution, which in other works is usually neglected, is now kept. We investigate the role of such a component by first using it to obtain a pointwise bound on the solution and then deploying it to construct a numerical scheme. The scheme obtained, besides being quasi-optimal in the L-2 sense, is also pointwise superconvergent in the temporal nodes. We prove a priori error estimates and we present numerical experiments to empirically support our findings.

• 出版日期2017-1