Coupled discontinuous and continuous Galerkin finite element methods for the depth-integrated shallow water equations

2004 ◽  
Vol 193 (3-5) ◽  
pp. 289-318 ◽  
Author(s):  
Clint Dawson ◽  
Jennifer Proft
Keyword(s):  
Finite Element ◽  
Shallow Water ◽  
Finite Element Methods ◽  
Shallow Water Equations ◽  
Galerkin Finite Element ◽  
Galerkin Finite Element Methods ◽  
Continuous Galerkin

scholarly journals Exponential convergence in $$H^1$$ of hp-FEM for Gevrey regularity with isotropic singularities

2019 ◽  
Vol 144 (2) ◽  
pp. 323-346 ◽  
Author(s):  
M. Feischl ◽  
Ch. Schwab
Keyword(s):  
Finite Element ◽  
Finite Number ◽  
Finite Element Methods ◽  
Exponential Convergence ◽  
Rates Of Convergence ◽  
Gevrey Regularity ◽  
Galerkin Finite Element ◽  
Galerkin Finite Element Methods ◽  
Continuous Galerkin ◽  
Exponential Rates

AbstractFor functions $$u\in H^1(\Omega )$$u∈H1(Ω) in a bounded polytope $$\Omega \subset {\mathbb {R}}^d$$Ω⊂Rd$$d=1,2,3$$d=1,2,3 with plane sides for $$d=2,3$$d=2,3 which are Gevrey regular in $$\overline{\Omega }\backslash {\mathscr {S}}$$Ω¯\S with point singularities concentrated at a set $${\mathscr {S}}\subset \overline{\Omega }$$S⊂Ω¯ consisting of a finite number of points in $$\overline{\Omega }$$Ω¯, we prove exponential rates of convergence of hp-version continuous Galerkin finite element methods on affine families of regular, simplicial meshes in $$\Omega $$Ω. The simplicial meshes are geometrically refined towards $${\mathscr {S}}$$S but are otherwise unstructured.

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