An \(L^p\)-DPG method with application to 2D convection-diffusion problems. (English) Zbl 1492.65319
Summary: This article summarizes the \(L^p\)-DPG method presented in our recent paper [Comput. Math. Appl. 95, 172–185 (2021; Zbl 1524.65833)], where only 1D convection-diffusion problems are solved. We apply the same computational techniques to 2D convection-diffusion problems and report additional numerical results herein. Furthermore, we propose an \(L^p\)-DPG method with variable \(p\) and illustrate it with numerical experiments.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
discontinuous Petrov-Galerkin methods; residual minimization; Banach spaces; convection-dominated diffusion; Fortin operators, \(p(\cdot)\)-LaplacianCitations:
Zbl 1524.65833References:
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