Estratégias p-Adaptativas para métodos DG hibridizados aplicados a problemas de ondas harmônicas no tempo

• Autor(a) principal: Mello, Leonardo Fagundes de
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/364
• topic: Método dos elementos finitos; Ondas sonoras; Ondas elásticas; Equação de Helmholtz; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE

P-adaptive algorithms based on hybrid finite element methods are proposed to approximate time harmonic wave problems. The mathematical problems consist in solving elliptic partial differential equations in two space dimensions that govern wave-scattering phenomena in the frequency domain in fluid, solid, and fluid-solid media where the frequency may or may not vary in space. We have adopted adaptively high orders for the degrees of local approximation polynomials, at the element level, and globally, on the edges of the mesh, through automatic decision rules, with the objective of reducing numerical pollution in regions where the frequency of the wave has high values. The automation adopted, composed of a priori and a posteriori strategies, consists of making decisions about the degrees of polynomials to be adopted on each element and at each edge of the mesh. We propose p adaptivity strategies for the problems of the acoustic wave, the elastic wave and for a fluid-structure interaction problem. We use continuous and discontinuous approximations for the multipliers, as well as continuous/discontinuous approximations that simultaneously employ both approaches on different subsets of edges of the mesh. We present results of numerical experiments comparing h and p convergence, a priori methodology for the primal Helmholtz problem, a posteriori approach to the mixed Helmholtz problem, and p adaptivity to approximate the coupled problem. These numerical experiments attest to the robustness of the approximations on regular, irregular and unstructured meshes.