2016/01/25 by Kristina Schwegler, Schwegler, Kristina, Marius Paul Bruchhäuser +3
Engineering · Mathematics · #65M12 #65M60 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1601.06544
openalex publication_date 2016/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The numerical approximation of convection-dominated problems continues to\nremain subject of strong interest. Families of stabilization techniques for\nfinite element methods were developed in the past. Adaptive techniques based on\na posteriori error estimates offer potential for further improvements. However,\nthere is still a lack in robust a posteriori error estimates in natural norms\nof the discretizations. Here we combine the dual weighted residual method for\ngoal-oriented error control with stabilized finite element approximations. By a\nduality argument an error representation is derived on that a space-time\nadaptive approach is built. It differs from former works on the dual weighted\nresidual method. Numerical experiments illustrate that our schemes are capable\nto resolve layers and sharp fronts with high accuracy and to further reduce\nspurious oscillations of approximations.\n