Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Finite Element Methods of Least-Squares Type
SIAM Review
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Least squares methods for solving differential equations using Bézier control points
Applied Numerical Mathematics
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
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In the last ten years, there has been significant improvement and growth in tools that aid the development of finite element methods for solving partial differential equations These tools assist the user in transforming a weak form of a differential equation into a computable solution Despite these advancements, solving a differential equation remains challenging Not only are there many possible weak forms for a particular problem, but the most accurate or most efficient form depends on the problem's structure Requiring a user to generate a weak form by hand creates a significant hurdle for someone who understands a model, but does not know how to solve it. We present a new algorithm that finds the solution of a partial differential equation when modeled in its strong form We accomplish this by applying a first order system least squares algorithm using triangular Bézier patches as our shape functions After describing our algorithm, we validate our results by presenting a numerical example.