arXiv subjects

Zhangxian Wang

Publications and source records attributed to Zhangxian Wang.

3 recordsLinked to original sources

arXiv2022

Quasi-optimal error estimates for the approximation of stable harmonic maps

Based on a quantitative version of the inverse function theorem and an appropriate saddle-point formulation we derive a quasi-optimal error estimate for the finite element approximation of harmonic maps into spheres with a nodal discretization of the unit-length constraint. The estimate holds under natural regularity requirements and appropriate geometric stability conditions on solutions. Extensions to other target manifolds including boundaries of ellipsoids are discussed.

math.NA↗

arXiv2022

Error analysis for the numerical approximation of the harmonic map heat flow with nodal constraints

An error estimate for a canonical discretization of the harmonic map heat flow into spheres is derived. The numerical scheme uses standard finite elements with a nodal treatment of linearized unit-length constraints. The analysis is based on elementary approximation results and only uses the discrete weak formulation.

math.NA↗

arXiv2020

Orthogonality relations of Crouzeix-Raviart and Raviart-Thomas finite element spaces

Identities that relate projections of Raviart-Thomas finite element vector fields to discrete gradients of Crouzeix-Raviart finite element functions are derived under general conditions. Various implications such as discrete convex duality results and a characterization of the image of the projection of the Crouzeix-Ravaiart space onto elementwise constant functions are deduced.

math.NA↗