Numerical Modelling and Capturing Singularities
|날짜Date||2019-05-24||시간Time||15:50 ~ 18:00|
|장소Place||Math. Bldg. 404||초청자Host||최민석|
|연사Speaker||Eun-Jae Park||소속Affiliation||Yonsei Univ.|
|TOPIC||Numerical Modelling and Capturing Singularities|
|소개 및 안내사항Content||Part 1.
Title: Numerical Modelling and Capturing Singularities
Mathematical models that involve convective and/or diffusive processes are
among the most widespread in all of science and engineering. The purpose of
this talk is to present what numerical modelling is about and to introduce finite element
methods for the numerical solution of partial differential equations in mechanics and physics.
We often encounter singularities from convection diffusion equations and/or the problem domain.
We introduce the idea of adaptive mesh refinement to efficiently capture singularities via a posteriori error analysis.
Several numerical examples will be presented.
Title: Staggered Galerkin Method: A New Computational Paradigm
Abstract: Finite element discretization of solutions with respect to simplicial/cubical meshes has been studied for decades, resulting in a clear understanding of both
the relevant mathematics and computational engineering challenges. Recently, there has been both a desire and need for an equivalent body of research regarding discretization with respect to generic polygonal/polytopal meshes. General meshes offer a very convenient framework for mesh generation, mesh deformations, fracture problems, composite materials, topology optimizations, mesh refinements and coarsening; for instance, to handle hanging nodes, different cell shapes within the same mesh and non-matching interfaces. Such a flexibility represents a powerful tool towards the efficient solution of problems with complex inclusions as in geophysical applications
or posed on very complicated or possibly deformable geometries as encountered in basin and reservoir simulations, in fluid-structure interaction, crack propagation or
In this talk, a new computational paradigm for discretizing PDEs is presented via staggered Galerkin method on general meshes. First, a class of locally conservative,
lowest order staggered discontinuous Galerkin method on general quadrilateral/polygonal meshes for elliptic problems are proposed. The method can be flexibly applied to rough grids such as highly distorted meshes. Next, adaptive mesh refinement is an attractive tool for general meshes due to their flexibility and simplicity in handling hanging nodes.
We derive a simple residual-type error estimator. Numerical results indicate that optimal convergence can be achieved for both the potential and vector variables, and the singularity can be well-captured by the proposed error estimator. Then, some applications to diffusion equations, Stokes equations, and linear elasticity equations are considered. Finally, we extend this approach to high-order polynomial approximations on general meshes.
Math Colloquium | Numerical Modelling and Capturing Singularities
수학과 | 2019.02.18 | 추천 0 | 조회 283
|Eun-Jae Park||Math. Bldg. 404|
Math Colloquium | Introduction to classification problems in distance-regular graphs
수학과 | 2019.02.18 | 추천 0 | 조회 300
|Sejeong Bang||Math. Bldg. 404|
Math Colloquium | Singular perturbations and boundary layers
수학과 | 2019.02.18 | 추천 0 | 조회 277
|Chang Yeol Jung||Math. Bldg. 404|
Math Colloquium | Introduction to convex real projective manifolds and orbifolds
수학과 | 2019.02.18 | 추천 0 | 조회 290
|Suhyoung Choi||Math. Bldg. 404|
Math Colloquium | Entangled Diophantine equations
수학과 | 2019.02.18 | 추천 0 | 조회 321
|Poo-Sung Park||Math. Bldg. 404|
Math Colloquium | Free Boundary Problems
수학과 | 2019.02.18 | 추천 0 | 조회 269
|Ki-Ahm Lee||Math. Bldg. 404|
Math Colloquium | Hyperbolic system of conservation laws
수학과 | 2019.02.18 | 추천 0 | 조회 309
|Moon-Jin Kang||Math. Bldg. 404|
Math Colloquium | Uncertainty principle, Hamiltonian dynamics and Gromov's nonsqueezing theorem
수학과 | 2019.02.18 | 추천 0 | 조회 298
|Yong-Geun Oh||Math. Bldg. 404|
Math Colloquium | Dedekind-Mertens Lemma
수학과 | 2019.02.20 | 추천 0 | 조회 309
|Byung Gyun Kang||Math. Bldg. 404|
Math Colloquium | 정년퇴임 기념강연
수학과 | 2019.02.12 | 추천 0 | 조회 387
|권용훈,심영선||Math. Bldg. 404|