In the present paper we initiate the study of hp Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size h and in the polynomial degree p in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included.
Basic principles of hp virtual elements on quasiuniform meshes / L. Beirão Da Veiga, A. Chernov, L. Mascotto, A. Russo. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 26:8(2016 Jul), pp. 1567-1598. [10.1142/S021820251650038X]
Basic principles of hp virtual elements on quasiuniform meshes
L. MascottoPenultimo
;
2016
Abstract
In the present paper we initiate the study of hp Virtual Elements. We focus on the case with uniform polynomial degree across the mesh and derive theoretical convergence estimates that are explicit both in the mesh size h and in the polynomial degree p in the case of finite Sobolev regularity. Exponential convergence is proved in the case of analytic solutions. The theoretical convergence results are validated in numerical experiments. Finally, an initial study on the possible choice of local basis functions is included.File | Dimensione | Formato | |
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