Based on H-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of fini...

Abstract To speed-up the solution of parametrized differential problems, reduced order models (ROMs) have been developed over years, including projection-based ROMs such as reduced-basis (RB) method, deep learning-based ROMs, well surrogate obtained through machine learning techniques. Thanks to its physics-based structure, ensured by use a Galerkin projection full model (FOM) onto linear low-d...

A postprocessing technique based on negative order norm estimates for the discontinuous Galerkin methods was previously introduced by Cockburn, Luskin, Shu, and Süli [Proceedings of the International Symposium on Discontinuous Galerkin Methods, Springer, New York, pp. 291– 300; Math. Comput., 72 (2003), pp. 577–606]. The postprocessor allows improvement in accuracy of the discontinuous Galerkin...

The standard in rod finite element formulations is the Bubnov–Galerkin projection method, where test functions arise from a consistent variation of ansatz functions. This approach becomes increasingly complex when highly nonlinear are chosen to approximate rod's centerline and cross-section orientations. Using Petrov–Galerkin we propose whole family nodal generalized virtual displacements veloc...

We provide an a priori error analysis of a wide class of finite element methods for the Stokes equations. The methods are based on the velocity gradient-velocity-pressure formulation of the equations and include new and old mixed and hybridizable discontinuous Galerkin methods. We show how to reduce the error analysis to the verification of some properties of an elementwise-defined projection a...