On Density and Approximation Properties of Special Solutions of the Helmohltz Equation
Georg J. Still · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1992
Abstract We consider eigenvalue problems for the Laplace operator on a region G. Especially if G is simply‐shaped, defect‐minimization methods with trial functions φ satisfying the Helmholtz equation Δφ + λφ = 0 may be suitable for the numerical solution of the problem. Such functions φ are given for example by the classical method of separation of variables. This paper is concerned with density and approximation properties of these special solutions of the Helmholtz equation with respect to the supremum‐norm.