A unified variational framework for elliptic PDEs with mixed Dirichlet–Neumann boundary conditions
Year: 2026
Type: article
Abstract: This paper presents a unified weak formulation for elliptic partial differential equations of the following form: [Formula: see text] subject to mixed boundary conditions consisting of prescribed Dirichlet data on a portion of the boundary and Neumann data on the remainder. By multiplying the strong form with finite element test functions and applying integration by parts, we derive a solvable variational problem that naturally incorporates both types of boundary conditions. The proposed formulation provides a direct pathway to numerical discretization, improves implementation efficiency, and is fully compatible with standard finite element procedures. Numerical applicability on general polygonal domains is emphasized, ensuring accurate and reliable simulations for practical boundary value problems.
Authors: K. V. Vidyasagar, S. Lalitha
Institution: Andhra University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7150901765