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Analysis and approximation of a two-dimensional induction heating problem
Gabriel R. Barrenechea, Katherine MacKenzie, Abner Salgado
In this paper, we analyse the existence of solutions and finite element approximation of a steady-state two-dimensional induction heating problem. One of the main difficulties of t…
Approximation of higher-order powers of the spectral fractional Laplacian via polyharmonic extension
Enrique Otárola, Abner J. Salgado
We use the polyharmonic extension approach to develop a numerical technique for discretizing higher-order powers of the spectral fractional Laplacian with .
The spectral fractional Laplacian with measure valued right hand sides: analysis and approximation
Enrique Otarola, Abner J. Salgado
We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduc…
Finite element approximation to linear, second order, parabolic problems with data
Gabriel Barrenechea, Abner J. Salgado
We consider the approximation to the solution of the initial boundary value problem for the heat equation with right hand side and initial condition that merely belong to . Du…
Finite element discretization of weighted -Laplace problems
Enrique Otarola, Abner J. Salgado
We study the finite element approximation of problems involving the weighted -Laplacian, where is an -function and the weight belongs to the class . In particular…