Orateur
Description
In this talk, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whose derivative is analytic and a finite sum of terms involving the logarithm of the modulus of a modified Weierstrass sigma function.
We implement the method using arbitrary precision and use the result to find approximate solutions to the Laplace problem and Steklov eigenvalue problem. Using a posteriori estimation, we show that the solution of the Laplace problem on a torus with a few holes has an error less than 10^(-100) using a few hundred degrees of freedom. The same estimates and precision are provided for Steklov eigenvalues computation.
In collaboration with C.-Y. Kao and B. Osting.
