Abstract

In this work we study a DPG method for an ultra-weak variational formulation of a reaction–diffusion problem. We improve existing a priori convergence results by sharpening an approximation result for the numerical flux. By duality arguments we show that higher convergence rates for the scalar field variable are obtained if the polynomial order of the corresponding approximation space is increased by one. Furthermore, we introduce a simple elementwise postprocessing of the solution and prove superconvergence. Numerical experiments indicate that the obtained results are valid beyond the underlying model problem.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.