Questions tagged [galerkin]

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0
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0answers
21 views

Reduce projection error while retaining similar amount of elements in CG-FEM

Based on the answers I got to my questions (Interpolation of function onto mesh gives different results, depending on mesh density and Solving a non-linear heat equation with the galerkin method gives ...
4
votes
1answer
136 views

Is a symmetric bilinear form necessary to ensure a weak formulation has a solution?

Problem I want to convert the general second order linear PDE problem \begin{align} \begin{cases} a(x,y)\frac{\partial^2 u}{\partial x^2}+b(x,y) \frac{\partial^2 u}{\partial y^2} +c(x,y)\frac{\...
0
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1answer
60 views

Interpolation of function onto mesh gives different results, depending on mesh density

I wanted to test the numerical accuracy of my program. For that I wanted to interpolate the function $$f=I_0\exp\left(-100x^2\right)\exp(-100y^2)$$ onto a grid, defined on $$\Omega=[0,1]^2$$ by using ...
3
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3answers
143 views

$H^1$-convergence rate of finite element method for Poisson equation, depending on element order

I wanted to verify my FEM-program by applying the method of manufactured solutions, while solving the Poisson equation in two dimensions using the continuous Galerkin method $$-\nabla^2u=f$$ with $$u=...
2
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0answers
30 views

Solving Compressible Euler in Primitive Variables with Galerkin P1 FEM

I have implemented a small compressible Euler solver, discretizing in primitive variables (rho, u, v, p) with standard Galerkin FEM P1 triangular elements, and mixed isotropic and anisotropic/...
2
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1answer
110 views

Prevent single node spikes in a FEM-simulation (using continuous Galerkin)

I am trying to solve a non-linear time-dependent heat equation $$\partial_tT=\nabla \left(k_T(T)\nabla T\right) + f$$ (similar to question Solving a non-linear heat equation with the galerkin method ...
2
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3answers
160 views

Role of weight function in Galerkin methods

I have difficulties in understanding the role of the weight function $w(x)$ that occurs in the solution of PDEs via the Galerkin approach. Consider a linear differential equation of the form $$ \...