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• W3046110143 abstract "In this paper we consider a fully discrete approximation of an abstract evolution equation, by means of a quasi non-conforming space approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the discrete solutions to weak solutions of the continuous problem. Hence, the result can be interpreted either as a justification of the numerical method or as an alternative way of constructing weak solutions. We set the problem in the very general and abstract setting of pseudo-monotone operators, which allows for a unified treatment of several evolution problems. Nevertheless, the paradigmatic example --which fits into our setting and which originated our research-- is represented by the $p$-Navier-Stokes equations, since the quasi non-conforming approximation allows to handle problems with prescribed divergence. Our abstract results for pseudo-monotone operators allow to show convergence just by verifying a few natural assumptions on the monotone operator (and its compact perturbation) time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be easily performed. The results of some numerical experiments are reported in the final section." @default.
• W3046110143 created "2020-08-03" @default.
• W3046110143 creator A5027944157 @default.
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• W3046110143 date "2020-07-30" @default.
• W3046110143 modified "2023-10-18" @default.
• W3046110143 title "Fully discrete, quasi non-conforming approximation of evolution equations" @default.
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• W3046110143 hasPublicationYear "2020" @default.
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